An experimental investigation of self-serving
biases in an auditing trust game: The effect of group affiliation

Ronald R. King
Washington University
St Louis, Missouri 63130

July 21, 2000

Helpful comments were received from Bryan Church, John Dickhaut, Nick Dopuch, Mahendra Gupta, Bill Messier, Mark Peecher, Bill Rankin, Chuck Schnitzlein, P.K. Sen, Ping Zhou, and seminar participants at Georgia State University, The Ohio State University, Washington University, and the First Asian Conference on Experimental Business Research held at HKUST. Research assistance was received from Amy Choy and Jim Holloway. Financial support from the Taylor Experimental Laboratory at the Olin School of Business is gratefully acknowledged.

Keywords: Self-serving bias; Auditor independence; and Experimental economics
Data Availability: Data are available from the author



An experimental investigation of self-serving biases in an
auditing trust game: The effect of group affiliation

Abstract

I report the results of an experiment designed to investigate self-serving biases in an audit trust game. My approach is to superimpose two different types of noneconomic factors (cheap talk/cheap action and group affiliation) in an economic setting to determine how the presence/absence of these two factors affect the formation of self-serving biases. I find that manager-subjects can use cheap talk/cheap action to induce auditor-subjects to display a self-serving bias. However, the self-serving bias is neutralized when auditor-subjects belong to groups that create social pressure to conform to group goals. Thus, psychological forces associated with group affiliation can undo the psychological-based self-serving bias. This finding calls into question the conclusion by Bazerman et al. (1997) that it is impossible for auditors to be independent because of self-serving biases.



An experimental investigation of self-serving biases in an
auditing trust game: The role of group affiliation

"[W]e maintain that audit failures are the natural product of the auditor-client relationship. Under current institutional arrangements, it is psychologically impossible for auditors to maintain their objectivity; cases of audit failure are inevitable, even with the most honest auditors"
Bazerman, Morgan, and Loewenstein (1997)

I. Introduction

In this paper I report the results of an experiment designed to investigate self-serving biases in an audit trust game. My motivation for this investigation is based on the extreme conclusion drawn by Bazerman et al. (1997) regarding audit quality as summarized in the quote shown above. Bazerman et al. (1997) argue that auditors cannot conduct impartial audits under existing auditor/client conditions because of a phenomenon known as self-serving bias. Self-serving bias, as the term is used by Bazerman et al. (1997), refers to a situation where people bias their decisions unconsciously.1 Bazerman et al. (1997) argue that auditors unintentionally lose objectivity because of their repeated and close interactions with client management and their limited and distant interactions with the investors who they supposedly represent. This conclusion could be of keen interest to both policy-makers and industry representatives who are debating whether the auditing industry is currently suffering from independence problems that reduce audit quality (MacDonald 1999; Report by the Panel on Audit Effectiveness 2000).

Unconscious actions by auditors that are biased can be more problematic than deliberate actions because deliberate ones may be reduced or eliminated by imposing economic sanctions, whereas unconscious biases cannot. Thus the arguments of Bazerman et al. (1997) deserve careful consideration, particularly because of several distinctive features of the auditing environment. The first feature relates to the timing and uncertainty of the consequences associated with agreeing or disagreeing with managers. Managers can apply immediate pressures (both economic and noneconomic) against an auditor who disagrees with them. However, economic penalties associated with the auditor agreeing with the client and thus issuing an erroneous audit report are often uncertain and delayed long into the future (Palmrose 1994). In addition, financial reporting standards are often vague and/or ambiguous, so auditors can find justification for their decisions (Libby et al. 2000). These factors combine to make the auditing environment conducive to self-serving biases.

Bazerman et al. (1997) review research that shows subjects do display self-serving biases in some experimental settings. In addition, they rightfully suggest that self-serving biases can be a powerful psychological force and that auditing services have characteristics that can increase the likelihood and strength of self-serving biases. However, their conclusion may be premature for two reasons. First, the experiments they summarize are not oriented to an auditing setting2 and second, the authors do not consider the fact that auditors have psychological bonds with other parties that can neutralize self-serving biases. For example, auditors generally belong to engagement teams, audit firms, and professional organizations that can create psychological affiliations that neutralize self-serving biases.3

My goal is to investigate self-serving biases in an experimental setting that is more closely related to auditing than the setting investigated by Bazerman et al. (1997) and one that is built on economic underpinnings. I begin my research by developing an "audit trust" game played by a manager-subject (M-subject) and an auditor-subject (A-subject). I incorporate in the model some features inherent in the practice of auditing that might exacerbate the creation of self-serving biases. In the game, each M-subject chooses a level of misappropriation (denoted as fraud for short). The A-subject's goal is to predict the M-subject's fraud level, because correctly anticipating fraud levels leads to an effective audit. The game is designed so that the A-subject's belief determines the cost of the audit, the probability of the A-subject incurring damages, and the probability of the M-partner facing sanctions. The M-subject's fraud level determines the amount of damages that the A-subject must pay if found liable.4

The audit trust game has a unique Nash equilibrium, which is Pareto dominated by a trust-cooperate combination (i.e., the A-subject trusts the M-subject to commit a low fraud level and the M-subject cooperates by committing a low fraud level). The payoffs are design so that M-subjects have incentives to increase fraud levels when A-subjects are expecting low levels of fraud, but A-subjects do not have incentives to change their level of trust if M-subjects commit low levels of fraud. These asymmetric payoffs create the economic incentives associated with trust in the game. Importantly, A-subjects benefit if paired with a trustworthy M-subject.

My second step is to operationalize the model in an experiment that follows the precepts of experimental economics5 (i.e., tying subject choices to their payoffs, having multiple replications of the game, paying subjects in private, etc) while incorporating features that can allow for the creation of self-serving biases. For example, in my setting, A-subjects receive delayed feedback about their M-partners' fraud levels. This delay makes it impossible for A-subjects to learn about the trustworthiness of their M-subject partners in the short run. In addition, my experimental setting allows M-subjects to create the appearance of trustworthiness in order to induce A-subjects to trust them.

To incorporate these features, I develop a full factorial, between-subjects experimental design with two treatments. The first treatment manipulates the interactions within each A- and M-subject pair in order to create different environments for A-subjects to trust M-subjects. The second one manipulates the strength of group bonds among A-subjects in order to create different levels of psychological costs associated with trust. My approach of investigating the effects of noneconomic factors in an economic setting is consistent with Kachelmeier's (1996a and 1996b) recommendation. However, my approach differs from previous research that investigates the extent to which economic incentives or market forces are able to reduce psychological biases (Duh and Sunder 1986). Rather, my approach is to create an economic setting and superimpose two different types of noneconomic phenomena to determine how the level of self-serving bias is changed based on the presence/absence of these two noneconomic forces. That is, I investigate whether one psychological-based factor (i.e., self-serving bias) can be neutralized by a different psychological-based factor (i.e., group affiliation) under the same economic setting.

The first treatment contrasts two settings that differ based on the type of interactions within each M- and A-subject pair; one treatment level is referred to as a weak pair setting and the other as a strong pair setting. Under the weak pair setting, M-subjects do not have the ability to explicitly communicate with their A-partners. Under this relatively stark information condition, A-subjects have limited reason to justify trusting M-subjects. Without a basis for trust, economic theory predicts that A-subjects will protect themselves by selecting the Nash strategy.

In the strong pair settings, each M-subject is allowed to communicate to his/her A-partner using two different nonbinding communication mechanisms: cheap action and cheap talk.6 Specifically, the cheap action mechanism allows the fraud levels chosen by M-subjects' to be observed by their A-subject partners after the first five rounds of interactions. This gives M-subjects the ability to form (false) reputations for committing low levels of fraud. The cheap talk option allows M-subjects to send nonbinding messages to their A-partners about their purported fraud levels. These two types of cheap communication may increase A-subjects' perception that their M-subject partners will cooperate, which raises the possibility of A-subjects displaying a self-serving bias by trusting their M-subject partners who may or may not be trustworthy. This treatment is to surrogate for the interactions between clients and auditors, where the interactions do not necessarily reflect the client's true trustworthiness (i.e., interactions on the golf course). In this setting, economic theory predicts that cheap action/talk should be ignored by subjects because these communication mechanisms are not credible (See Cooper et al. 1989; 1992 and for research investigating cheap talk in a variety of settings). However, psychological-based arguments suggest that cheap action/talk can create a level of familiarity and thus facilitate trust formation (Libby et al 2000). I measure self-serving bias as the excess level of A-subjects' trust over that found under the weak pair setting. In addition, I measure the extent to which M-subjects take advantage of this self-serving bias by increasing their levels of fraud.

The group treatment contrasts two settings relating to the strength of group bonds among the A-subjects-one treatment level is referred to as a weak group setting and the other as a strong group setting. Under the weak group setting, A-subjects do not interact in any organized way with each other during the experimental session. Thus, under the weak group setting, the interactions are strictly between A- and M-subjects. Under the strong group setting, A-subjects become members of a group that creates social pressures for conformance to group goals. This is operationalized by having A-subjects interact during the instruction period and A-subjects are informed that the person with the highest damage amount at the end of the session will be identified to the other A-subjects. This strong group manipulation is intended to create cohesion and a shared group norm among A-subjects, which in turn increases the psychological cost of damages.7 The perception of the cost of damages increases because high damages can result in identification, which is psychologically costly because it results in the loss of face (see Kachelmeier and Shehata 1997 for a discussion of face saving). Although the psychological costs change under the strong group setting, the economic incentives do not.8 Manipulating the psychological ties among A-subject groups allows me to investigate whether the self-serving bias can be mitigated when A-subjects are part of a group that creates psychological bonds to compete with the (cheap) reputations created within M- and A subject pairs.

I report the decisions from 44 M- and A-subject pairs: eleven pairs under each of the four settings (Weak pair/Weak group; Strong pair/Weak group; Weak pair/Strong group; Strong pair/Strong group). University students participated as subjects in the experiment. The results clearly indicate a self-serving bias under the Strong pair/Weak group setting. That is, the use of cheap talk and cheap action by M-subjects under the Strong pair/Weak group setting increases A-subjects' willingness to trust M-subjects over that of the Weak pair/Weak group setting. M-subjects in turn commit higher levels of fraud under the Strong pair/Weak group setting due to this (undeserving) trust. In a second comparison, I contrast A-subjects' beliefs under the Weak pair/Weak group setting with those from the Weak pair/ Strong group setting. I find that A-subjects under the strong group setting exhibit significantly less trust of M-subjects than A-subjects under the Weak pair/Weak group setting and this in turn induces M-subjects to commit less fraud under the WP/SG setting. Thus, the group treatment changes A-subjects' behavior based solely on noneconomic pressures. In yet another comparison, I contrast A-subjects' beliefs under the Strong pair/Weak group with the Strong pair/Strong group setting. I find that the self-serving bias exhibited under the Strong pair/Weak group setting is neutralized under the Strong pair/Strong group setting.

There are three primary contributions to this research. First, my research challenges the conclusion by Bazerman et al. (1997) that it is impossible for auditors to be independent because of self-serving biases. Although self-serving bias can affect decision-making in the manner suggested by these authors, this bias can be mitigated by group affiliations. One implication of my finding is that accounting firms should continue to undertake efforts to create and maintain strong group cohesion among audit teams.

A second contribution of my research is the recognition that although economic forces may not completely offset certain psychological biases (Camerer 1997), it is possible that noneconomic forces can counter such biases.9 Although the motivation for my research is based on Bazerman et al's conclusion about self-serving bias, my approach of investigating tradeoffs created by different psychological-based factors is general and can be applied to other settings. An example relates to investigating how motivated reasoning is affected by conflicting goals (Kadous, Kennedy, and Peecher 2000). A third contribution is the development of an experimental setting that incorporates various features consistent with the audit environment (although the features are admittedly stylized, as in any model). The first feature is that auditors benefit from having trustworthy clients, but they may not be able to determine the true trustworthiness of a client in the short run. The second is the asymmetric incentives between the manager and auditor and the asymmetric information, which creates ambiguity about the incentives of the other player. Thus, my setting provides a parsimonious setting for investigating auditing issues that have both economic and noneconomic components.

The paper proceeds as follows. In the next section I provide a discussion of the model. The experimental treatments and method are discussed in the third section followed by the development of hypotheses in section 4. The results are presented in section 5. Section 6 provides an overview and a discussion of limitations and possible future research avenues.

II. Model

In this section, I present the audit trust game that underlies the experiment. The game focuses on the economic forces-the psychological forces will be manipulated in the experimental design.

Setup of the stage game

I assume that there are two active players, a manager (denoted as M for purposes of the model) and an auditor (denoted as A for purposes of the model). The following timeline summarizes the stage game played by the two parties. Subjects will play multiple stage games during the experiment.

t=1 M is endowed with financial resources and selects a fraud level (i.e., selects an amount of resources to misappropriate). Simultaneously, A forms a belief about M's fraud level.
t=2 An audit is conducted based on A's belief of M's fraud level.

t=3

If the audit detects fraud, M is sanctioned.

t=4

If fraud is committed and the audit does not detect it, A may be liable for damages. A will not learn about the damages until the end of the series of stage games.

In the first step of the game (t=1), M receives X units of currency that M should transfer to an unmodeled third party (denoted as the investor).10 M selects a fraud level, f (f >0) which is the fraction of X that is stolen by M, rather than transferred to the investor.

A, who is paid a flat fee of Y, is responsible for monitoring M, with the objective of increasing the amount of money M transfers to the investor. The belief formed by A of M's fraud level is denoted as fA and is the sole input to the audit. Specifically, A's audit will detect M's fraud with probability q(fA). The cost of the audit increases as A's beliefs about M's fraud level increases.11 When the audit does detect fraud, M is sanctioned for an amount denoted as S(f)X. Under those cases when M is sanctioned, A never pays damages (i.e., does not bear liability). If the audit does not detect the fraud (with probability of 1- q(fA)), M retains fX and the court can find A liable for damages of D(f) with probability _. A learns about his/her damages at the end of the final round of the series of stage games (to be consistent with the fact that feedback about litigation damages comes to auditors much later than the time of the audit). Table 1 summarizes the notation used in the model.


Table 1: Notation for the Model and Experiment

Notation

Used to represent

A

Auditor

M

Manager

Y

A's auditing fee

C(q(fA))

A's audit cost based on A's belief of M's fraud

Probability that A bears liabilities when M is not sanctioned

D(f)

Damages amount A faces

fA

A's beliefs of M's fraud level, f

f1A

Trust choice (0.483)

f2A

Nash choice (0.6964)

f3A

Defensive choice (0.8844)

Z

Resources that belong to M

X

Amount held by M to be transferred to investors

q(fA)

Probability that M is sanctioned

S(f)X

Sanction amount for M when the audit detects M committing fraud

fX

Amount retained by M if M is not sanctioned

f

M's fraud level

f1

Cooperate choice (0.483)

f2

Nash choice (0.6964)

f3

Cheat choice (0.8844)

   


The Auditor's Objective Function

The auditor's objective function is shown below. The auditor selects a belief about M's fraud level to maximize profits by minimizing expected costs.

(1)

where:

Y is A's fee;

f A is A's belief about M's fraud level;

q(f A ) is the audit technology which is a function of A's belief;

C(q(f A )) is the cost of the audit, which is a function of A's belief and the audit technology;

is the exogenous probability that A is found liable and must pay damages to the investor; and

D(f) is the damage amount (as an increasing function of M's fraud level) that A must pay to the investor if found liable by the court.

To summarize the relevant factors inherent in A's objective function-A's belief, f A, affects the cost of the audit and the probability of A incurring damages. M's action, f, affects the amount of damages that A must pay if found liable.

The Manager's Objective Function

M is in possession of financial resources X + Z, of which X should be transferred to the investor. M can steal some fraction of X, (denoted fX); however, if caught, M will be sanctioned for an amount equal to S(f)X. The objective of M is to select a fraud level, f, to maximize expected returns, as shown below:

(2)

where:

Z is the amount of financial resources that belongs to M;

f is M's fraud level;

q(f A) is the probability of M being sanctioned;

X is the amount held by M that should be transferred to the investor; and

S(f)X is the amount of M's sanction if the audit detects fraud.

To summarize the relevant factors inherent in M's objective function-M's action, f, affects the amount of cash M retains and the amount of his/her sanction. A's action, fA, affects the probability of M retaining the misappropriated resources or facing a sanction.

Equilibrium predictions for the above game depend on the conjectures each player makes about the other player (Kreps 1990). Given full information about the other player's choices, a Nash equilibrium can be calculated using the conventional approach of setting the first derivative of M and A's objective functions to zero, and solving for f A and f (and verifying the sign of the second order conditions). I discuss the information environment for the subjects and the implications of information asymmetry on the equilibrium in more detail below. However, I first explain how the above model is converted into the discrete choice game that is operationalized in the experiment.

Converting the general game to the experimental game

To operationalize the general game for the experiment, I choose functions and parameters consistent with the assumptions of the model. Table 2 summarizes these functions and parameters. For example, the cost function, C, is set to aq2 (shown in the second row of Table 2) and the audit technology, q is set to bf A (shown in row 3). Column 2 shows the constraints and column 3 shows the actual parameters used.

Each player is restricted to three choice options in the experiment. This is done to simplify the game for subjects and to provide clearer demarcations for comparisons across settings. The three fraud/belief options are 0.483 (denoted as f1 for M and f1A for A), 0.6964 (denoted as f2 for M and f2A for A), and 0.8844 (denoted as f3 for M and f3A for A).12 Thus, for example, at the f1 level, M misappropriates 48.3 percent of the investor's assets. I next use the objective functions of the two players to create payoffs for each of the three fraud and belief levels. I begin with the auditor's payoffs.

To calculate the payoffs for A, I begin with the objective function shown in equation 1. This equation indicates A's payoffs depend on whether A pays damages. If A does not pay damages, the expected payoffs are a function of the no-liability payoff and the associated probability of no liability, as shown below.


Payoff to A with no liability

Probability of A having no liability


The payoff amount includes the fixed fee, Y, minus the cost of the audit, C(q(f A )). The probability of A not having liability is shown as the probability of detecting the fraud, q(f A) plus the probability of not detecting the fraud and the court finding A not liable, (1 - q(f A))(1 - )). Substituting the specific functions from Table 2 (but not the parameter values) yields:


Payoff to A with no liability

Probability of A having no liability



Table 2: Functions, Constraints, and Parameters Used in the Model and Experiment

Functions Used in Model

Constraints on Functions

Experimental Parameters

a > 0

a = 76

b > 0

b = 0.6

 

1 > > 0

= 0.267

d > 1, X > 0

d = 2.25, X = 152

k1 1

k1 = 1

Y = constant

 

Y = 60

Z = constant

 

Z = 5


Next, the specific parameters are substituted. Table 2, row 7 shows that the audit fee is set to 60. Other parameters include a=76, b=0.6, and =0.267. For purposes of this example, A's belief and M's fraud level are set to (f1A, f1), the case where A trusts M to cooperate (i.e., f1A = 0.483) and M does cooperate (i.e., f1=0.483). Substituting the parameters yields;


Payoff to A with no liability for

the choice pair (f1A,f1)

Probability of A having no liability for

the choice pair (f1A,f1)


Multiplying the payoff amount of 53.6 by the probability of having no liability of 0.8103 yields 43.44, which is A's expected payoff when A selects f1A without liability. I now calculate A's expected payoffs when A bears liability. The amount and the probability are shown below.


Payoff to A with liability

Probability of A having liability


The payoff is the fixed fee, Y, minus the cost of the audit, C(q(f A )), minus damages, D(f). The probability of liability is (1 - q(f A)), which is the probability of not detecting the fraud multiplied by the probability of the court assessing liability. Substituting the functional forms yield:


Payoff to A with liability

Probability of A having liability


Substituting the appropriate parameters and the values for f1A and f1 yields:


Payoff to A with liability for

the choice pair (f1A,f1)

Probability of A having liability for

the choice pair (f1A,f1)


Multiplying the amount of -111.63 by the probability of 0.1896 yields -21.16 which is A's expected payoff when the choice pair is (f1A, f1) and A bears liability. Thus, summing these two amounts (43.44 - 21.16) gives A's expected payoff of 22.28 for selecting f1A when M chooses f1.

I now calculate the payoffs for M, following the same approach. Using M's objective function shown in equation 2, I begin by calculating the expected payoffs when M is not sanctioned. The amount and probability are shown below:


Payoff to M with no sanction

Probability of M having no sanction


Z represents M's resources and fX represents the amount stolen. The probability, 1- q(f1A), reflects the frequency that the audit fails to detect the fraud. Substituting the specific functions from Table 2, yields the following:


Payoff to M with no sanction

Probability of M having no sanction


Substituting the specific parameter values for f1A and f1 yields:


Payoff to M with no sanction for

the choice pair (f1A, f1)

Probability of M having no sanction for

the choice pair (f1A, f1)


Multiplying the amount (78.42) by the probability (0.7102) yields 55.70. This is M's expected payoff when the choice pair is (f1A, f1) and the M is not sanctioned. I next show the calculations when M is sanctioned.


Payoff to M with sanction

Probability of M having sanction


The payoff includes Z minus the sanctioned amount S(f)X with the probability that A detects the fraud. Substituting the functions, yield:


Payoff to M with sanction

Probability of M having sanction


Substituting the parameters for f1A and f1 yields:


Payoff to M with sanction for

the choice pair (f1A, f1)

Probability of M having sanction for

The choice pair (f1A, f1)


Multiplying the payoff amount (-30.46) by the probability (0.2898) yields -8.84, which is M's expected payoff when the choice pair is (f1A, f1) and M is sanctioned. Thus, summing the two amounts (-8.84 + 55.70) yields the expected payoff of 46.86 for M.

Table 3 shows the calculations for the eighteen payoffs (9 payoffs for A and 9 for M). The table subdivides the payoffs based on whether M is sanctioned and/or whether A pays damages. For example, the first row of the table shows the payoffs for (f1A, f1) when M is sanctioned. This outcome occurs with a probability of 0.29, and provides a payoff of 53.61 for A and -30.48 for M. The fourth row show the expected payoffs for (f1A, f1), as calculated above (A's payoff is 22.32 and M's payoff is 46.82).13 The 18 expected payoffs from Table 3 are summarized in the expected payoff matrix shown below, which is used in the experiment. The expected payoff matrix shows A's expected payoffs in the bottom left of each cell and M's expected payoff in the top right. For example, in the upper left-hand cell (f1A, f1), Player A has an expected payoff of 22.32 and M has 46.82. In essence, this matrix contains expected payoffs generated by combining parameters and function consistent with the assumptions of the model presented above. To simplify the discussion I refer to the three belief options/choices as Trust, Nash, and Defensive and the three fraud levels as Cooperate, Nash, and Cheat.


Table 3: Calculations of each Cell in the Expected Payoff Matrix

 

Auditor

Manager

 

Probability

Amount

Expected Payoffs

Probability

Amount

Expected Payoffs

f = f1, fA = f1A, M sanctioned

0.29

53.61

15.54

0.29

-30.48

-8.84

f = f1, fA = f1A,
M not sanctioned

A bears no liability

0.52

53.61

27.91

0.71

78.44

55.70

A bears liability

0.19

-111.63

-21.16

Expected payoffs for (f1, f1A)

   

22.28

   

46.86

             

f = f1, fA = f2A, M sanctioned

0.42

46.73

19.53

0.42

-30.48

-12.74

f = f1, fA = f2A,
M not sanctioned

A bears no liability

0.43

46.73

19.94

0.58

78.44

45.66

A bears liability

0.16

-118.51

-18.42

Expected payoffs for (f1, f2A)

   

21.05

   

32.92

             

f = f1, fA = f3A, M sanctioned

0.53

38.60

20.48

0.53

-30.48

-16.18

f = f1, fA = f3A,
M not sanctioned

A bears no liability

0.34

38.60

13.28

0.47

78.44

36.82

A bears liability

0.13

-126.64

-15.87

Expected payoffs for (f1, f3A)

   

17.89

   

20.64

             

f = f2, fA = f1A, M sanctioned

0.29

53.61

15.54

0.29

-68.73

-19.93

f = f2, fA = f1A,
M not sanctioned,

A bears no liability

0.52

53.61

27.91

0.71

110.87

78.73

A bears liability

0.19

-184.58

-35.00

Expected payoffs for (f2, f1A)

   

8.45

   

58.80

             

f = f2, fA = f2A, M sanctioned

0.42

46.73

19.53

0.42

-68.73

-28.72

f = f2, fA = f2A,
M not sanctioned

A bears no liability

0.43

46.73

19.94

0.58

110.87

64.54

A bears liability

0.16

-191.47

-29.76

Expected payoffs for (f2, f2A)

   

9.71

   

35.81

             

f = f2, fA = f3A, M sanctioned

0.53

38.60

20.48

0.53

-68.73

-36.47

f = f2, fA = f3A,
M not sanctioned

A bears no liability

0.34

38.60

13.28

0.47

110.87

52.03

A bears liability

0.13

-199.60

-25.01

Expected payoffs for (f2, f3A)

   

8.75

   

15.56

             

f = f3, fA = f1A, M sanctioned

0.29

53.61

15.54

0.29

-113.90

-33.02

f = f3, fA = f1A,
M not sanctioned,

A bears no liability

0.52

53.61

27.91

0.71

139.43

99.01

A bears liability

0.19

-248.86

-47.18

Expected payoffs for (f3, f1A)

   

-3.74

   

65.99

             

f = f3, fA = f2A, M sanctioned

0.42

46.73

19.53

0.42

-113.90

-47.60

f = f3, fA = f2A,
M not sanctioned

A bears no liability

0.43

46.73

19.94

0.58

139.43

81.17

A bears liability

0.16

-255.75

-39.75

Expected payoffs for (f3, f2A)

   

-0.28

   

33.57

             

f = f3, fA = f3A, M sanctioned

0.53

38.60

20.48

0.53

-113.90

-60.44

f = f3, fA = f3A,
M not sanctioned

A bears no liability

0.34

38.60

13.28

0.47

139.43

65.44

A bears liability

0.13

-263.88

-33.07

Expected payoffs for (f3, f3A)

   

0.69

   

5.00

The numbers in this table are not exactly the numbers in the normal form game shown in the text of the paper because values are rounded in order to have consistency in the extensive form and normal form of the game.


Expected Payoff Matrix Used in the Experiment

 

M's fraud level

f1

(Cooperate)

f2

(Nash)

F3

(Cheat)

A's beliefs of

M's fraud level

f1A

(Trust)

46.82

58.76

65.96

22.32

8.51

-3.67

f2A

(Nash)

32.89

35.78

33.55

21.08

9.75

-0.22

f3A

(Defensive)

20.62

15.55

5.01

17.92

8.79

0.74



Nash equilibrium and possible focal points

Inspecting the payoff matrix of this audit trust game indicates the Nash equilibrium is the belief/ fraud combination (f2A, f2). This outcome represents the solution where each player best responds to his/her anticipation of the other player's choice and neither party has a unilateral incentive to defect. Under this equilibrium, the expected payoffs to A and M are 9.75 and 35.78, respectively.

A possible focal point is the trust-cooperate combination (f1A, f1), with payoffs to A and M of 22.31 and 46.82, respectively. This outcome Pareto dominates the Nash equilibrium (f2A, f2). That is, both parties are better off under this combination than under the Nash combination. However, under the trust-cooperate combination, M has incentives to select the cheat option, (and increases expected payoffs to 65.96) which reduces A's expected payoffs to -3.67. On the other hand, A has no incentives to deviate from his/her trust belief if M selects the cooperate option, f1. Under this asymmetric payoff structure, A-subjects benefit from having trust-worthy clients. A third possible outcome is the defensive-cheat choice pair (f3A, f3). Under this outcome, M is indifferent to committing and not committing fraud given the chance of being detected by A (the expected payoff of 5 is M's endowment of Z). These options are discussed in more detail in the hypothesis section. In the next section I present the experimental methods.

III. Experimental Methods and Design

Subjects are business school student volunteers who are paid for their participation based on their choices and those of their counterpart. Either ten or twelve subjects participate in each session, half of them playing the role of the manager-subject (denoted as M-subject for discussion related to the experiment) and half playing the role of the auditor-subject (denoted as A-subject for discussion related to the experiment). Two sessions are run under each of the four settings. These eight sessions produce a total of 11 subject-pairs for each of the four experimental settings, which is shown below.


Experimental design

Auditor

Group

Treatment

Strong Group

WP/SG

SP/SG

Weak Group

WP/WG

SP/WG

   

Weak pair

Strong pair

   

Pair Treatment

Each experimental session is conducted on networked PCs, with privacy maintained for each subject, except when noted below. The instructions and experiment do not use terms that have real world connotation, such as fraud or auditor (see Haynes and Kachelmeier 1998 for a discussion of this issue).14 Rather, M-subjects are referred to as A players and A-subjects are referred to as B players. The instructions are available upon request. All M-subjects have special training several days prior to the actual experimental sessions to help them gain experience with the experiment. During the training session, M-subjects gain experience by participating in a series of practice rounds, playing both roles. This process helps them develop a more complete understanding of the incentives for both players. The trained M-subjects could participate in multiple sessions of the actual experiment. For the actual experiment, A-subjects arrive at the experimental laboratory one-half hour earlier than M-subjects and receive their instructions prior to the arrival of M-subjects. Upon arrival of the M-subjects, the instructions are summarized to both M- and A-subjects to enhance common knowledge of the game.


The following outlines how the treatments were operationalized in the experiment.


 

Procedures for creating group ties among A-subjects

Phase 1 - Cheap Action Phase: 5 rounds

Phase 2 - Regular Play Phase: 18 or 19 rounds

Phase 3 - M's actions disclosed to A and Resolution Phase: 6 rounds

Experimental Setting

WP/WG

(Weak pair/ Weak group)

No

No

No cheap talk

Yes

SP/WG

(Strong pair/ Weak group)

No

Yes

Cheap talk

Yes

WP/SG

(Weak pair/ Strong group)

Yes

No

No cheap talk

Yes

SP/SG

(Strong pair/ Strong group)

Yes

Yes

Cheap talk

Yes


The first column identifies the four experimental settings, and rows 2-5 show the four settings. The remaining columns summarize how I operationalize the treatments. The second column indicates how settings differ with respect to the A-subject group treatment. Under the WG settings, A-subjects are given instructions collectively, but without any overtures that they are part of a group. Under the SG settings, group cohesion is established by asking A-subjects to introduce themselves to the group of A-subjects, to use nametags, to select a team name, and to work together on the quiz. A-subjects are also told that the group member who has the highest level of damages at the end of the session will have his/her name posted on the board. This treatment is entirely psychological in that there are no explicit economic ties among the A-subject group members.

The third column indicates how settings differ with respect to the pair treatment. Only subjects under the SP settings complete Phase 1: the cheap action phase. Specifically, during the cheap action phase, each M- and A-subject pair interact for 5 rounds (following the sequence of steps discussed in the theory section above) and both parties receive a fixed payment of $0.50 per round. Subjects are informed that the fixed payment is independent of the decisions they make during this phase. At the end of the fifth round, each A-subject observes the choices of his/her M-partner. This allows M-subjects the ability to form reputations for cooperation by selecting the cooperate option (hence the "cheap action" designation). In addition, during phase 1 M-subjects can use cheap talk, which will be discussed below. The purpose of the cheap action phase is to enhance trust formation between M- and A-subjects. To further facilitate this trust, the cheap action phase is referred to as the "Get Acquainted" session for the subjects. A-subjects learn his/her M-partner's choice at the end of the cheap action phase, which gives M-subjects the opportunity to condition A-subject's expectations. This treatment surrogates for interactions between clients and auditors that do not necessarily reflect the client's true trustworthiness.

The fourth column deals with Phase 2: regular play. This phase consists of 18 or 19 rounds of play (subject are not informed of the number of rounds in this phase) where subjects earn money based on the outcomes of their joint decisions. The sequence of each round follows the steps discussed in the theory section above. Under the SP settings M-subjects can engage in cheap talk during the regular play phase. Cheap talk is operationalized by allowing M-subjects to send to their A-partners the message "I will chose 1 this round." If M-subjects elect not to send this message, the message "No message this round" is sent. This restriction is implemented to limit M-subjects' communications options so that they can only communicate their willingness to cooperate (rather than allowing them to create communication "noise" that may be difficult for me to decipher ex post). Throughout the experiment, each A-subject learns when his/her M-partner is sanctioned (i.e., found to have committed fraud) but not the amount of the sanction.15 Thus, for rounds when M-subject is sanctioned, each A-subject knows that he/she will not pay damages; however, this sanction information is not informative because the frequency of sanctions is based entirely on A's belief (see Table 3 for the probabilities).16 In contrast, when the M-subject is sanctioned, he/she learns the belief that his/her A-partner selected, but the A-subject does not know that the M-subject learns the belief. In addition, A-subjects know M-subjects' expected payoffs (from the payoff matrix), but do not amounts that go into the expected payoffs. Thus, A-subjects are at an information disadvantage, relative to M-subjects.

The approach of not informing A-subjects that their M-partners receive information about A-subjects' belief (when fraud is detected) is an attempt to lessen A-subjects' ability to signal their belief to M-subjects and thus become a leader, as in a leader/follower game.17 This stark information condition faced by the A-subjects limits them from forming a justifiable basis for trusting M-subjects. A-subjects learn about M's fraud level only at the end of the regular play phase, thus making it impossible to update using either a Bayesian or fictitious play approach. However, M-subjects do receive information about their A-partners beliefs, thus allowing them to best respond. Thus, under this setting, A-subjects can only guess their M-partners' fraud levels while M-subjects could best respond to their A-partners' beliefs.

At the end of the regular play phase, each A-subject is informed of his/her M partner's choices, but not his/her actual level of liability. The purpose of this procedure is to determine the extent to which A-subjects modify their behavior after observing the strategies of their M-subject partners, but not the consequences of the actions. Each pair then continues for another six rounds of play, denoted as the resolution phase.18 At the end of the resolution phase, A-subjects are informed of their liabilities, net earnings for each round, and total cash earnings. Finally all subjects are paid privately and dismissed. For settings under the strong group settings, the A-subject with the largest cumulative damages is identified to the other subjects.

Figures 1 and 2 display the screens for M-subjects and A-subjects for the SP/SG setting, respectively. Note that M-subjects are denoted as Player A and A-subjects are denoted as Player B in the experiment. The screen for M-subjects has four windows. The "game tree" window (upper left-hand side), the "average payoff table" window (upper right-hand side), the "message to player B" window (bottom left-hand side), and the "history" window (bottom right-hand side). I begin by describing the average payoff table window shown in the upper right-hand side of the screen. This is the screen that subjects use to select their choices. In addition, this window shows the expected payoff matrix for all nine fraud/belief combinations. Note that in Figure 1, action 3 (cheat) and belief 1 (trust) have been selected. The screen highlights the expected payoffs for both players (the payoffs to the M-subject is the bottom row) for this choice combination.

The game tree window in the upper left-hand side of the screen shows the probabilities and the amounts for strategy combinations selected in the average payoff table. As noted above, the cheat-trust combination is selected in the average payoff table. The left branch of the game tree shows the payoffs to the M-subject if the fraud is not detected by the auditor (this is denoted as Inflow). The probability of no liability is 0.71 and payoff to the M-subject is 139.29 for the combination of (f1A, f3). The right branch shows the probability of fraud being detected (denoted as Outflow) is 0.29 and payoffs to the M-subject is -113.75 if fraud is detected. The expected value of these two possibilities is shown as 65.96. The game tree is updated each time the subject selects a different strategy combination in the average payoff table window.

The "message to player B" window on the bottom left is displayed only under SP settings and is used by M-subjects to send messages to A-subjects about their intended actions. The "history" window shows the history of play for past rounds. For the case shown in Figure 1, the M-subject selected action 1 in round 1 and this generated a payoff of 78.43 (the M-subject is not sanctioned). In round 2, the M-subject chose option 2 and is sanctioned, receiving -68.64 for this round. In round 3, the M-subject chose option 3 and is not sanctioned, receiving 139.29. Figure 2 shows the A-subject's screen (for a different M-partner than shown in Figure 1) and is interpreted in the same way as discussed for M-subjects. Note that in the history screen, the A-subject observes his/her payoffs for a round only if the M-subject has fraud detected (in this example the M-subjects' fraud is detected in rounds 2 and 3). In the next section, I present the hypotheses.


Figure 1: M-subject's Computer Screen Under Strong Pair/Strong Group Setting

Figure 2: A-subject's Computer Screen Under Strong Pair/Strong Group Setting

IV. Hypotheses

In this section, I present six sets of hypotheses. The first five hypotheses relate to predictions comparing subjects' decisions during the regular play phases of the four settings. The first set of hypotheses focuses on the beliefs of A-subjects under the WP/WG setting. The purpose of this set of hypotheses is to establish a benchmark to which other settings will be compared. Self-serving bias is defined as the increase in trust beliefs in the other settings over that established in the WP/WG setting. The second set of hypotheses compares the SP/WG setting to the WP/WG setting to evaluate the extent to which self-serving bias is created by the strong pair treatment under the WP setting. The third set of hypotheses compares the WP/SG setting to the WP/WG setting to evaluate the effect of the strong group treatment. The fourth set of hypotheses compares the SP/SG setting to the WP/WG setting to investigate the strong pair effect combined with the strong group treatment. The fifth set of hypotheses compares the SP/SG setting to the SP/WG setting to investigate the effect of the group treatment under the SP setting. The sixth set of hypotheses compares A-subjects' beliefs during the regular play phase to the beliefs during the resolution phase. The objective of this comparison is to study the extent to which A-subjects change their beliefs after receiving information about M-subjects' choices (but not the consequences of the choices).

H1: Hypotheses for the WP/WG setting (baseline setting)

The first set of hypotheses investigates A-subject beliefs during the regular play phase of the WP/WG setting. Consistent with previous experimental research, I specify the null hypothesis to predict that beliefs are selected randomly. Rejecting this (strawman) hypothesis shows that A-subjects select definable patterns of behavior. The first alternative is the Nash prediction and is based on the game-theoretic reasoning presented above. Under the Nash equilibrium, A-subjects are assumed to analyze the expected payoffs for both parties and to recognize the incentives M-subjects have to defect from a cooperate choice. The experiment is designed to limit the trust-cooperate pair (and thus increase the likelihood of the Nash outcome from an economic point of view) by providing A-subjects with limited and asymmetric information about M's fraud level. Specifically, the following procedures are implemented in the experiment to create information asymmetry between the two players:

As mentioned above, the stark information condition faced by A-subjects limits them from forming a justifiable basis for trusting M-subjects. Without a basis for trust, economic theory predicts that A-subjects will protect themselves by selecting the Nash belief, f2A. Technically, the Nash prediction is that f2A will be chosen 100% of the time, but previous research shows that such an extreme prediction is unsubstantiated (King and Schwartz 2000). Thus, I test the Nash prediction by investigating whether f2A is chosen more than 33% of the time.

The second alternative hypothesis predicts that A-subjects trust M-subjects and select a relatively higher percentage of trust beliefs. This outcome is optimal for A only if the M-subject cooperates (which is not learned by A-subjects until the end of the regular play phase). The rationale for the trust alternative is based on previous economic experiments that indicate subjects trust others to reciprocate more than predicted by economic theory in noncooperative games (Berg et al.1995; Dawes and Thaler 1988; McCabe, Rassenti, and Smith 1998). As stated above, the trust-cooperate pair (f1A, f1) Pareto dominates the Nash equilibrium. The null and two competing hypotheses for WP/WG setting are stated below:

H1(Null): A-subjects' beliefs are random (leading to uniform distribution of beliefs).
H1(Nash): A-subjects select the Nash belief (f2A) more than 33% of the time.
H1(trust): A-subjects select the trust belief (f1A) more than 33% of the time.

H2: WP/WG compared to SP/WG (effect of strong pair under the weak group setting)

The second set of hypotheses deals with predictions about the SP/WG setting relative to the WP/WG setting. Under the SP/WG setting, M-subjects can use cheap action and cheap talk to attempt to induce A-subjects to trust him/her. Recall that during the cheap action phase, each player received a flat payment of $0.50 each round independent of the decision he/she made. At the end of the cheap action phase, each A-subject observes his/her M-partner's fraud level for those rounds. Knowing this, M-subjects could attempt to build trust during the cheap talk phase by sending the (cheap talk) message "I will chose 1 this round" and by selecting the cooperate choice, f1. This gives M-subjects the possibility of conditioning the expectations of the A-subjects during the cheap action phase. In addition, each M-subject can further condition his/her partner's expectations during the regular play phase by sending the cheap talk message "I will chose 1 this round".

Previous experimental research has shown that nonbinding communications can enhance mutual cooperation in coordination games where both parties benefit from cooperation (Cooper et al. 1989). In addition, research has shown that certain types of cheap talk can enhance cooperation in a prisoners' dilemma game, where players have symmetric payoffs and both can credibly commit to punish a defector. However, the audit trust game differs from the coordination and prisoners' dilemma games because of asymmetric payoffs and information. Thus, the reliance on cheap talk that existed in coordination and prisoners' dilemma games may not be observed in my setting.19

However, cheap action/talk may be a useful coordination mechanism in my setting if M-subjects are trustworthy. If A-subjects perceive their M-partners to be trustworthy (due to cheap talk/action), the expected damages to the A-subject are perceived to be lower. This in turn should induce the A-subject's to select the trust belief and both players benefit, relative to the Nash combination. The benefits to A-subjects from coordination with M-subjects can be seen by considering the A-subject's objective function (which is reproduced below). The only element in the objective function that cheap talk/action affects is D(f), which is determined by the M-subject. If the A-subject expects low damages because the M-subject cooperates, the A-subject's best response is to trust.

(1-reproduced)

To test whether cheap action combined with cheap talk creates an environment for self-serving bias to exist, I compare A-subjects' beliefs under the SP/WG settings with those from the WP/WG setting. If A-subjects choose the trust belief more frequently under the SP/WG setting than under the WP/WG setting (and M-subjects do not reciprocate by cooperating), I conclude that self-serving bias is created by the cheap talk/cheap action treatment. Under both settings, economic theory suggests that A-subjects know M-subjects' incentives and anticipate their strategies, and thus cheap action/ talk should not affect the beliefs of A-subjects. The null and the competing hypotheses are stated below:

H2(Null): There are no differences between A-subjects' beliefs across the WP/WG and SP/WG settings.
H2(SSB): A-subjects select the trust belief, f1A, more frequently under the SP/WG setting than under the WP/WG setting.

The difference between the levels of the trust belief chosen under the SP/WG and the WP/WG settings will serve as a baseline measure of self-serving bias.

H3: WP/WG compared to WP/SG (effect of strong group)

The third set of hypotheses deals with the strong group effect under the WP setting. The strong group manipulation is intended to create cohesion among A-subjects (from having name tags, working together on the quiz, etc.), which in turn increases the social pressure to conform to group goals and raises the psychological cost of liability. Thus, subjects can "save face" by selecting the defensive belief (see Ho 1976 for a discussion of face saving). Kachelmeier and Shehata (1997) find that the observability of actions can influence behavior in some setting.

There are several ways to incorporate this psychological cost into an A-subject's objective function, but a simple approach is to add a cost that is perceived by an individual A-subject i to be a relative comparison of his/her own decisions to other A-subjects decisions, denoted as j (shown as G in the A-subject's modified objective function shown below). Of course there are various ways to model the effect of group membership, but the important element is that the expected cost of liability increases.

(3)

Thus, if the procedures used under the SG setting are salient, A-subjects will perceive an additional cost and thus trust M-subjects less under the SG setting than under the WG setting. However, if A-subjects do not attach any psychological cost to identification, the economics should dominate and the SG setting should not differ from the WG setting. The null and competing hypotheses are stated below:

H3(Null): There are no differences between A-subjects' beliefs across the WP/WG and WP/SG settings.
H3(Group effect): A-subjects tend to trust their counterpart less (i.e., increase their selection of the Nash belief, f2A and/or the defensive belief, f3A) under the WP/SG setting than under the WP/WG setting.

H4: WP/WG compared to SP/SG (effect of strong pair and strong group)

The fourth set of hypothesis compares A-subjects' beliefs across the WP/WG and SP/SG settings. The null hypothesis states that there are no differences between A-subjects' beliefs under WP/WG and SP/SG settings because strong pair effect neutralizes the strong group effect. The alternative makes a nondirectional prediction that the two forces will not completely balance each other out. In the results I investigate various ways the two settings can differ, including the effects on M-subjects' choices. The null and the alternative hypotheses are stated below:

H4(Null): There are no differences between A-subjects' beliefs across the WP/WG and SP/SG settings.
H4(Group effect does not perfectly neutralizes the Pair effect): A-subjects' beliefs under the WP/WG and SP/SG settings are different.

H5: SP/WG compared to SP/SG (effect of strong group treatment under the strong pair settings)

Under this set of hypotheses I investigate whether the self-serving bias (if it exists) under the SP/WG setting can be reduced by the strong group treatment. Specifically, the alternative predicts that the strong group effect is salient under the strong pair setting, thus neutralizing the self-serving bias. The arguments for the above hypotheses applies, thus making this set of hypotheses a "horse race" between the noneconomic forces. The null and competing hypotheses are stated below:

H5(Null): There are no differences between A-subjects' beliefs across the SP/WG and SP/SG settings.
H5(Group effect): A-subjects under the SP/SG setting are less trusting than A-subjects under the SP/WG setting.

H6: Comparing A-subjects' beliefs from the resolution rounds to the regular play rounds

A-subjects are informed of his/her M-partner's choices at the end of the regular play phase, but not his/her own actual level of liability. H6 investigates the effect of this information on A-subjects' belief selection. The null hypothesis predicts that there will be no differences between A-subjects' choices during the regular play rounds and those from the resolution rounds. This is consistent with the notion that A-subjects expect M-subjects to be untrustworthy and the information of the fraud level of M-subject does not change A-subjects' beliefs (i.e., A-subject beliefs are in "steady state"). The alternative predicts that A-subjects will change their frequency of choosing the trust belief after learning M-subjects' fraud level. The alternative is based on the fact that A-subjects do not have information about the M-subjects during the regular play rounds, and thus may be overly trusting of M-subjects during the regular play phase.

H6(Null): A-subjects' frequency of selecting the trust belief, f1A, will be the same across the regular play phase and the resolution phase.
H6(Alternative): A-subjects' frequency of selecting the trust belief, f1A, will decrease across the regular play phase and the resolution phase.

V. Results

Table 4 summarizes both players' choices under the four settings for the regular play and resolution phases. Using the WP/WG setting as an example to interpret the table, Row 1 of Panel A shows that A-subjects choose the trust belief, f1A, 85 times out of 203 opportunities (42%), the Nash belief, f2A, 69 times (34%), and the defensive belief, f3A, 49 times (24%). The fourth column shows that there are 203 decisions20 made by A-subjects during the regular play phase and column 5 shows that the average belief is 1.82 (calculated by setting f1A = 1, f2A = 2, f3A = 3). My primary analysis investigates proportions of aggregate belief/fraud levels for subjects. This data aggregation approach is used to highlight the general tendencies of the data. A second data aggregation method would be to define an observation as the cumulated decisions of a subject. There are eleven subject-pairs in each setting; thus generating a total of 44 individual subject observations. The results using 44 observations produces lower significance levels, but the same qualitative results. In general, statistical tests performed on experimental data are used to supplement results that are recognizable using an "interocular test" which is the intent in this paper. See Davis and Holt (1993) for a discussion of statistical analysis of experimental data.

Row 5 of Panel A of Table 4 shows A-subjects' choices during the resolution phase of WP/WG. The frequencies (percentage) that each belief is chosen are 23 (35%), 17 (26%), and 26 (39%) for trust, Nash, and defensive belief, respectively, with 66 choice opportunities,21 and an average belief of 2.05. Row 1 of Panel B shows that the frequencies of each fraud level selected by M-subjects during the regular play phase of the WP/WG setting are 49 (24%), 61 (30%), and 93 (46%) for the cooperate, Nash, and cheat fraud choices, respectively, and average fraud of 2.22 (calculated by setting f1 = 1, f2 = 2, f3 = 3). M-subjects' choices during the resolution phase are shown in Row 5 of Panel B as 26 (40%), 16 (24%), and 24 (36%) for cooperate, Nash, and cheat, respectively, and with the average fraud of 1.97. Figures 3-6 graphically presents the data from the regular play phase.


 

Table 4. A-subjects' Beliefs and M-subjects' Fraud Levels for the Four Settings subdivided into Regular Play and Resolution Phases

 
               

Panel A: A-subjects' Beliefs

         

Regular Play Phase

Trust
f1A

Nash
F2A

Defensive
f3A

Total

Average Belief2

 
 

WP/WG1

85 (42%)

69 (34%)

49 (24%)

203

1.82

 
 

SP/WG

139 (68%)

22 (11%)

42 (21%)

203

1.52

 
 

WP/SG

61 (31%)

39 (20%)

98 (49%)

198

2.19

 
 

SP/SG

97 (48%)

31 (15%)

75 (37%)

203

1.89

 
               

Resolution Phase

           
 

WP/WG

23 (35%)

17 (26%)

26 (39%)

66

2.05

 
 

SP/WG

31 (47%)

10 (15%)

25 (38%)

66

1.91

 
 

WP/SG

18 (28%)

10 (16%)

36 (56%)

64

2.28

 
 

SP/SG

19 (29%)

14 (21%)

33 (50%)

66

2.21

 
               

Panel B: M-subjects' Fraud Level

         

Regular Play Phase

Cooperate
f1

Nash
f2

Cheat
f3

Total

Average Fraud Level3

 
 

WP/WG

49 (24%)

61 (30%)

93 (46%)

203

2.22

 
 

SP/WG

49 (24%)

28 (14%)

126 (62%)

203

2.38

 
 

WP/SG

81 (41%)

49 (25%)

68 (34%)

198

1.93

 
 

SP/SG

51 (25%)

48 (24%)

104 (51%)

203

2.26

 
               

Resolution Phase

           
 

WP/WG

26 (40%)

16 (24%)

24 (36%)

66

1.97

 
 

SP/WG

31 (47%)

22 (33%)

13 (20%)

66

1.73

 
 

WP/SG

16 (25%)

16 (25%)

32 (50%)

64

2.25

 
 

SP/SG

22 (33%)

26 (40%)

18 (27%)

66

1.94

 
               

1 WP/WG = Weak Pair Weak Group setting
SP/WG = Strong Pair Weak Group setting
WP/SG = Weak Pair Strong Group setting
SP/SG = Strong Pair Strong Group setting
2 Average beliefs are calculated by setting f1A = 1, f2A = 2, f3A = 3.
3 Average fraud levels are calculated by setting f1 = 1, f2 = 2, f3 = 3.


Results for H1: Hypotheses for the WP/WG setting (establishing a baseline setting for A-subjects' beliefs)

This hypothesis investigates A-subjects' beliefs under the WP/WG setting. The analysis is summarized in Table 5. Panel A addresses H1(null), which predicts that A-subjects' beliefs are uniformly distributed across the three belief options. There are 203 A-subject observations under this regime and thus the predicted frequency for each belief choice is 67.67, if uniformly distributed. As shown in Panel A, the actual frequencies (percentages) for the regular play phase are 85 (42%), 69 (34%), and 49 (24%) for the trust, Nash, and defensive belief, respectively. The hypothesis that these choices are uniformly distributed is rejected (p<0.01) using a chi-square test. This finding motives an investigation of the patterns chosen by A-subjects.22

Panel B of Table 5 investigates the two competing hypotheses. The Nash alternative hypothesis predicts that A-subjects will select f2A more than 33% of the time. I use 33% as a benchmark for both the Nash alternative and the Trust alternative to standardize the comparisons between the two competing hypotheses. As shown in Panel B of Table 5, the Nash belief is chosen 34% of the time. Using a one-tailed test of proportions, A-subjects' choices of the Nash belief is not significantly different from 33%, indicating that A-subjects do not choose the Nash option more frequently. Panel B also shows the results of a one-tailed test of proportions for H1(Trust), which predicts that f1A will be chosen more than 33% of the time. I find support for this hypothesis (p<0.008), indicating that the trust belief is chosen more frequently under the WP/WG setting. I will discuss mean beliefs and fraud levels later in this section.

Panel C of Table 5 investigates the extent to which the beliefs of A-subjects correspond to M-subjects' fraud levels. Recall that the payoffs for the A-subjects are designed such that A-subjects maximize profits by selecting a belief that corresponds his/her M-partner's chosen fraud level (i.e., f*A = f. For the WP/WG setting, I first determine whether A-subjects' beliefs differ from M-subjects' fraud levels by comparing the frequency of each belief chosen by A-subjects (denoted as #(fiA)) to the frequency of each fraud level chosen by M-subjects (denoted as #(fj)). I find the frequency of A-subjects' beliefs do not equal the proportion of M-subjects' fraud levels, using a chi-square test (p<0.00). I next apply a one-tailed test of proportions to examine how the two sets of proportions differ. As shown in Panel C of Table 5, I find that A-subjects select a higher proportion of the trust belief than M-subjects select the cooperate choice (p<0.00) and M-subjects select a higher proportion of the cheat choice than A-subjects select the defensive belief (p<0.00). There is no significant difference between the proportion of Nash choices for the two players.

Figure 3 graphically displays the data under the WP/WG setting. The figure reinforces the results from Table 5 that A-subjects select the trust belief most frequently and M-subjects select the cheat choice most frequently. The results indicate a mismatch that is detrimental to the A-subjects. The fact that A-subjects trusts M-subjects (and M-subjects do not deserve the trust) could be interpreted as a type of self-serving bias. However, as discussed below, I define self-serving bias as the increase in the trust belief by A-subject under a setting, relative to the WP/WG setting.


 

Table 5: Examination of H1(Null), H1(Nash), and H1(Trust)- Establishing a Benchmark for the Weak Pair/ Weak Group Setting (Regular Play Phase)

 
 

Panel A

Examination of H1(Null)

   
 

H1(Null):

Are A-subjects' beliefs random under the WP/WG setting?

 
 

2 - test

 

Trust
f1A

Nash
f2A

Defensive
f3A

Total

Average
beliefs

 
 

Actual frequency

85 (42%)

69 (34%)

49 (24%)

203

1.82

 
 

Expected frequency

67.67

67.67

67.67

203

   
     

Pr(X2 )=

0.008

Conclude: beliefs are not random

 
                 
 

Panel B

Examination of H1(Nash) and H1(Trust)

   
 

H1(Nash):

Do A-subjects select f2A more than a third of the time?

 
 

H1(Trust):

Do A-subjects select f1A more than a third of the time?

 
 

One-tailed test of proportions

Trust
f1A

Nash
f2A

 
   

Proportion

0.42

0.34

 
   

Expected

0.33

0.33

 
   

Z-score

2.39

0.12

 
   

Pr(Z Zc)

0.008

0.451

 
   

Conclude

Trust beliefs are selected more than 1/3 of the time

Nash beliefs are not selected more than 1/3 of the time

 
                 
 

Panel C

Do A-subjects' beliefs differ from M-subjects' fraud levels under the WP/WG setting?

 
       
 

2 - test

 

(#(f1A), #( f1))

(#(f2A), #( f2))

(#(f3A), #( f3))

     
 

WP/WG

 

(85, 49)

(69, 61)

(49, 93)

     
     

Pr(X2 )=

0.000

Conclude: choices differ

 
                 
 

One-tailed test of proportions

(#(f1A), #( f1))

(#(f2A), #( f2))

(#(f3A), #( f3))

   
   

Proportion

(0.42, 0.24)

(0.34, 0.30)

(0.24, 0.46)

   
   

Difference

0.17

0.03

-0.21

   
   

Z-score

3.69

0.74

4.47

   
   

Pr(Z Zc)

0.000

0.228

0.000

   
   

Conclude

Proportions differ

Proportions do not differ

Proportions differ

   
                 
                 


Results for H2: Hypotheses comparing the WP/WG setting to the SP/WG setting (what is the effect on A-subjects' beliefs of the strong pair treatment under the weak group setting?)

Table 6 provides a summary of the test results for H2. Panel A shows that during the regular play phase of the SP/WG setting, the frequencies (percentages) of trust, Nash, and defensive beliefs chosen by A-subjects are 139 (68%), 22 (11%), and 42 (21%) respectively. Panel A also shows a chi-square test comparing A-subjects' choices under the SP/WG and WP/WG settings. The null hypothesis of no differences is rejected (p<0.00), indicating that A-subjects' beliefs differ across the two settings. Before I discuss how A-subjects' choices differ across the two settings, I first compare A-subjects' beliefs with M-subjects' fraud levels under the SP/WG setting.

Panel B of Table 6 presents this comparison and shows that A-subjects' beliefs differ significantly from M-subjects' fraud levels (p<0.00). A one-tailed test of proportions reported in Panel B shows that the proportion of A-subjects' trust beliefs differ significantly from the proportion of M-subjects' cooperate choices and also the defensive beliefs and cheat choices (p<0.00). However, the proportion of A- and M-subjects' Nash choices do not differ significantly. That is, A-subjects trust M-subjects more frequently, while M-subjects cheat more frequently. Figures 3 and 4 are graphical representations of A-subjects' beliefs for the two setting for the regular play phase. Note the visible spike at the trust-cheat combination under the SP/WG setting relative to the WP/WG setting.

Panel C of Table 6 builds on panel A by investigating A-subjects' choice differences under the SP/WG and WP/WG settings. Using a one-tailed test of proportions, I find the trust and Nash beliefs differ (p<0.00) across the two settings, but not the defensive belief (p<0.238). Specifically, results from the one-tailed test show that A-subjects choose the trust belief more frequently under the SP/WG setting but the Nash belief more frequently under the WP/WG setting, indicating that A-subjects under the SP/WG setting have a significantly higher level of self-serving bias. This finding is consistent with the findings of Bazerman et al. (1997) that decision-makers can be induced to reveal a self-serving bias. In this case, cheap action and cheap talk on the part of M-subjects increase the level of trust by A-subjects under the SP/WG setting over that of the WP/WG, even though trust increases A-subjects' potential risk of liability.

Panel D shows the frequencies and percentages of M-subjects' fraud levels under the SP/WG and WP/WG settings. A chi-square test shows that M-subjects' choices differ significantly across the two settings (p<0.00). Panel E of Table 6 shows M-subjects do not differ in their proportion of cooperate choices, but do for the Nash and cheat choices (p<0.00). M-subjects under the SP/WG setting select the cheat choice 62% of the time (126 times out of 203 opportunities), versus 46% (93 times out of 203 opportunities) under the WP/WG setting. This 16% difference can be interpreted the additional fraud generated due to A-subjects' trust of M-subjects.


 

Table 6: Examination of H2 - Comparing the Strong Pair/Weak Group Setting
to the Weak Pair/Weak Group Setting (Regular Play Phase)

   
 

Panel A

             
 

H2(Null):

Do A-subjects' beliefs differ across the WP/WG and SP/WG settings?

 

2 - test

 

Trust
f1A

Nash
f2A

Defensive
f3A

Total

Average
Beliefs

 
 

WP/WG

 

85 (42%)

69 (34%)

49 (24%)

203

1.82

 
 

SP/WG

 

139 (68%)

22 (11%)

42 (21%)

203

1.52

 
     

Pr(X2 )=

0.000

Conclude: beliefs differ

 

Panel B

           
 

Do A-subjects' beliefs correspond to M-subjects' fraud levels under SP/WG setting?

 
 

2 - test

 

(#(f1A), #( f1))

(#(f2A), #( f2))

(#(f3A), #( f3))

   
 

SP/WG

 

(139, 49)

(22, 28)

(42, 126)

   
     

Pr(X2 )=

0.000

Conclude: choices do not correspond

 

One-tailed test of proportions

(#(f1A), #( f1))

(#(f2A), #( f2))

(#(f3A), #( f3))

 
   

Proportion

(0.68, 0.24)

(0.11, 0.14)

(0.21, 0.62)

 
   

Difference

0.44

-0.02

-0.41

 
   

Z-score

8.86

0.76

8.36

 
   

Pr(Z _Zc)

0.000

0.225

0.000

 
   

Conclude:

Choices differ

Choices not differ

Choices differ

 
                 
 

Panel C

             
 

H2(SSB):

Do A-subjects trust M-subjects more under the SP/WG setting than under the WP/WG setting?

 
 

One-tailed test of proportions

Trust
f1A

Nash
f2A

Defensive
f3A

   
   

WP/WG

85/203 = 0.42

69/203 = 0.34

49/203 = 0.24

   
   

SP/WG

139/203 = 0.68

22/203 = 0.11

42/203 = 0.21

   
   

Z-score

5.29

5.47

0.71

   
   

Pr(Z Zc)

0.000

0.000

0.238

   
     

Conclude: different levels of trust

 
 

Panel D

             
 

Do M-subjects' fraud levels differ across the WP/WG and SP/WG settings?

 

2 - test

 

Cooperate
f1

Nash
f2

Cheat
f3

Total

Average fraud

 
 

WP/WG

 

49 (24%)

61 (30%)

93 (46%)

203

2.22

 
 

SP/WG

 

49 (24%)

28 (14%)

126 (62%)

203

2.38

 
     

Pr(X2 )=

0.000

Conclude: choices differ

   
 

Panel E

             
 

How do M-subjects' fraud levels differ across the SP/WG and WP/WG settings?

 
 

One-tailed test of proportions

Cooperate
f1

Nash
f2

Cheat
f3

   
   

WP/WG

49/203 = 0.24

61/203 = 0.30

93/203 = 0.46

   
   

SP/WG

49/203 = 0.24

28/203 = 0.14

126/203 = 0.62

   
   

Z-score

-0.12

3.84

3.19

   
   

Pr(Z Zc)

0.546

0.000

0.001

   
 

Conclude: increase in the frequency of the cheat choice under SP/WG

 
     


Results for H3: Hypotheses comparing the WP/WG setting to the WP/SG setting (what is the effect on A-subjects' beliefs of the strong group treatment under the weak pair setting?)

Table 7 provides a summary of the test results for H3. Panel A shows that during the regular play phase of the WP/SG setting, the frequencies (percentages) of trust, Nash, and defensive beliefs selected by A-subjects are 61 (31%), 39 (20%), and 98 (49%) respectively. For the same setting, the frequencies (percentages) of cooperate, Nash, and cheat choices selected by M-subjects are 81 (41%), 49 (25%) and 68 (34%) respectively (shown in Table 4). Figure 5 shows the combination of A-subjects' and M-subjects' choices under the WP/SG setting.


 

Table 7: Examination of H3 - Comparing the Weak Pair/Strong Group Setting
to the Weak Pair/Weak Group Setting (Regular Play Phase)

 
 

Panel A

             
 

H3(Null):

Are there differences between A-subjects' beliefs in the WP/WG and WP/SG settings?

 

2 - test

 

Trust
f1A

Nash
f2A

Defensive
f3A

Total

Average beliefs

 
 

WP/WG

 

85 (42%)

69 (34%)

49 (24%)

203

1.82

 
 

WP/SG

 

61 (31%)

39 (20%)

98 (49%)

198

2.19

 
     

Pr(X2 )=

0.000

Conclude: beliefs differ

   
 

Panel B

             
 

Do A-subjects' beliefs correspond to M-subjects' fraud levels under the WP/SG setting?

   
 

2 - test

 

(#(f1A), #( f1))

(#(f2A), #( f2))

(#(f3A), #( f3))

     
 

WP/SG

 

(61, 81)

(39, 49)

(98, 68)

     
     

Pr(X>2) =

0.009

Conclude: choices do not correspond

 
 

One-tailed test of proportions

(#(f1A), #( f1))

(#(f2A), #( f2))

(#(f3A), #( f3))

   
   

Proportion

(0.31, 0.41)

(0.20, 0.25)

(0.49, 0.34)

   
   

Difference

-0.10

-0.05

0.15

   
   

Z-score

1.99

1.09

2.95

   
   

Pr(Z Zc)

0.023

0.138

0.002

   
   

Conclude:

Choice differs

Choice do not differ

Choice differs

   
                 
 

Panel C

             
 

Are A-subjects' are more distrusting under the WP/SG setting?

 
 

One-tailed test of proportions

Trust
f1A

Nash
f2A

Defensive
f3A

   
   

WP/WG

85/203 = 0.42

69/203 = 0.34

49/203 = 0.24

   
   

WP/SG

61/198 = 0.31

39/198 = 0.20

98/198 = 0.49

   
   

Z-score

2.20

3.11

5.16

   
   

Pr(Z Zc)

0.014

0.001

0.000

   
     

Conclude: less trust under WP/SG

   
 

Panel D

             
   

Are there differences between M-subjects' fraud levels under the WP/WG and WP/SG settings?

 

2 - test

 

Cooperate
f1

Nash
f2

Cheat
f3

Total

Average fraud

 
 

WP/WG

 

49 (24%)

61 (30%)

93 (46%)

203

2.22

 
 

WP/SG

 

81 (41%)

49 (25%)

68 (34%)

198

1.93

 
     

Pr(X2 )=

0.001

Conclude: choices differ

   
                 
 

Panel E

             
   

Do M-subjects committed less fraud under WP/SG than under the WP/WG setting?

 
 

One-tailed test of proportions

Cooperate
f1

Nash
f2

Cheat
f3

   
   

WP/WG

49/203 = 0.24

61/203 = 0.30

93/203 = 0.46

   
   

WP/SG

81/198 = 0.41

49/198 = 0.25

68/198 = 0.34

   
   

Z-score

3.30

1.23

2.43

   
   

Pr(Z Zc)

0.000

0.110

0.007

   
 

Conclude: most cooperate choices and less cheat choices under WP/SG

 


Panel A in Table 7 shows that the null hypothesis of no differences in A-subjects' beliefs across the two settings is rejected (p<0.00) using a chi-square test. In Panel B, the results from a chi-square test shows that A- subjects' beliefs differ from M-subjects' fraud levels under the SG/WP setting ((p<0.009). A one-tail test of proportions show that there are significant differences in the frequency of matched choices between the trust belief and cooperate choice and between the defensive belief and the cheat choice, but not for the Nash choices. Specifically, the proportion of M-subjects' cooperate choices is significantly higher than the proportion of A-subjects' trust beliefs and the reverse is true of the cheat choice and defensive belief. That is, A-subjects do not trust M-subjects even though the M-subjects are more trustworthy under this setting.

Panel C of Table 7 builds on panel A by investigating A-subjects' beliefs under the WP/WG and WP/SG settings. Using a one-tailed test of proportions, I find the proportion of each belief differs across the two settings (p<0.014). Specifically, results from the one-tailed test show A-subjects choose the trust and Nash beliefs more frequently and the defensive belief less frequently under the WP/WG setting. This indicates that A-subjects under the WP/SG setting have a significantly lower level of self-serving bias than A-subjects under the SP/WG setting. This finding suggests that the group manipulation is salient.

Panel D shows the frequencies and percentages of M-subjects' fraud levels under the WP/WG and WP/SG settings. A chi-square test shows M-subjects' choices differ significantly across the two settings (p<0.001). Panel E of Table 6 shows M-subjects choices under the two settings differ in their proportions of cooperate and cheat choices (p<0.007), but not in the proportion of Nash choices. M-subjects under the WP/WG setting select the cheat choice 46% of the time (93 times out of 203 opportunities) versus 34% (68 times out of 203 opportunities) under the WP/SG setting. That is, the group treatment decreases the trust of A-subjects, which in turn lowers the level of fraud committed by M-subjects. In this case, the 12% difference represents the decrease in fraud caused by the group treatment on A-subjects. Figure 5 shows that under the WP/SG setting, there is a perceptible increase in the defensive-cooperate combination over that of the WP/WG setting shown in Figure 3.

Results for H4: Hypotheses comparing the WP/WG setting to the SP/SG setting (what is the effect of the strong group treatment on A-subjects' beliefs under the strong pair setting?)

Table 8 summaries the results for H4. Panel A shows that during the regular play phase of the SP/SG setting, the frequencies (percentages) of trust, Nash, and defensive beliefs selected by A-subjects are 97 (48%), 31 (15%), and 75 (37%) respectively. Under the same setting, the frequencies (percentages) of cooperate, Nash, and cheat choices selected by M-subjects are 51 (25%), 48 (24%), and 104 (51%) respectively (see Table 4). Figure 6 shows the A-subjects' and M-subjects' choice combinations under the SP/SG setting.

Panel A in Table 8 reports the results of the chi-square test showing a significant difference between A-subjects' beliefs across the WP/WG and SP/SG settings (p<0.00). This finding indicates that the group effect may either be weaker or stronger than the pair effect. Panel C shows the results of the one-tailed test of proportions comparing each belief. This pair-wise comparison shows significant differences for A-subjects' Nash and defensive beliefs across the two settings (p<0.00). Specifically, A-subjects under the WP/WG setting select the Nash belief more frequently and the defensive belief less frequently than A-subjects under the SP/SG setting. This implies that A-subjects are less trusting of M-subjects under the SP/SG setting. However, the proportions of the trust belief selected by A-subjects are not significantly different under the two settings (p<0.14). This is noteworthy because it indicates that the strong group manipulation neutralizes the self-serving bias created by the strong pair manipulation. In addition, the results show that although there is not a difference in the proportion of trust, A-subjects are more defensive under the SP/SG setting.

In Panel B of Table 8, a chi-square test shows that A- and M-subject choices differ under the SG/SP setting (p<0.000) and a one-tail test of proportions show that there is a significant difference in each of A-subjects' beliefs and corresponding M-subjects' fraud levels (p<0.022). Panel D shows the frequencies and percentages of M-subjects' fraud levels under the WP/WG and SP/SG settings. A chi-square test shows M-subjects' choices do not differ significantly across the two settings. Thus, under the SP/SG setting, A-subjects select a similar proportion of trust beliefs (but different proportions of Nash and defensive beliefs) than under the WP/WG setting and this induces M-subjects do have similar fraud levels across the two regimes.


 

Table 8: Examination of H4 - Comparing the Strong Pair/Strong Group Setting
to the Weak Pair/Weak Group Setting (Regular Play Phase)

 
 

Panel A

             
 

H4(Null-A):

Are there differences between A-subjects' beliefs across the WP/WG and SP/SG settings?

 

2 - test

 

Trust
f1A

Nash
f2A

Defensive
f3A

Total

Average beliefs

 
 

WP/WG

 

85 (42%)

69 (34%)

49 (24%)

203

1.82

 
 

SP/SG

 

97 (48%)

31 (15%)

75 (37%)

203

1.89

 
     

Pr(X2 )=

0.000

(Reject H4(Null))

   
 

Panel B

             
   

Do A-subjects' beliefs correspond to M-subjects' fraud levels under the SP/SG setting?

   
 

2 - test

 

(#(f1A), #( f1))

(#(f2A), #( f2))

(#(f3A), #( f3))

     
 

SP/SG

 

(97, 51)

(31, 48)

(75, 104)

     
     

Pr(X2 )=

0.000

Conclude: choices do not correspond

 
 

One-tailed test of proportions

(#(f1A), #( f1))

(#(f2A), #( f2))

(#(f3A), #( f3))

   
   

Proportion

(0.48, 0.25)

(0.15, 0.24)

(0.37, 0.51)

   
   

Difference

0.22

-0.08

-0.14

   
   

Z-score

4.64

2.01

2.80

   
   

Pr(Z Zc)

0.000

0.022

0.003

   
   

Conclude

Choices differ

Choices differ

Choices differ

   
                 
 

Panel C

             
 

H4(Trust):

Are A-subjects' less trusting under the SP/SG setting?

 
 

One-tailed test of proportions

Trust
f1A

Nash
f2A

Defensive
f3A

   
   

WP/WG

85/203 = 0.42

69/203 = 0.34

49/203 = 0.24

   
   

SP/SG

97/203 = 0.48

31/203 = 0.15

75/203 = 0.37

   
   

Z-score

1.10

4.26

2.69

   
   

Pr(Z Zc)

0.136

0.000

0.004

   
     

Conclude: no difference in trust choice

   
 

Panel D

             
   

Are there differences between M-subjects' fraud levels under the WP/WG and SP/SG settings?

 

2 - test

 

Cooperate
f1

Nash
f2

Cheat
f3

Total

Average
Fraud

 
 

WP/WG

 

49 (24%)

61 (30%)

93 (46%)

203

2.22

 
 

SP/SG

 

51 (25%)

48 (24%)

104 (51%)

203

2.26

 
     

Pr(X2 )=

0.332

Conclude: choices do not differ

   
                 


Results for H5: Hypotheses comparing A-subjects' beliefs under the SP/WG and SP/SG settings (does self-serving bias that arises under the SP/WG setting decrease due to the strong group treatment?)

Table 9 summaries the results for H5 with Panel A showing a chi-square test comparing A-subjects' beliefs under the two settings. The null of no differences between A-subjects' beliefs under the SP/WG and SP/SG settings is rejected (p<0.00). Also shown in the bottom part of Panel A is a comparison of A-subjects' responses to their M-partners' cheap talk proposals under the two settings. M-subjects sent 192 and 170 messages to signal cooperation during the regular play phase under the SP/WG and SP/SG settings, respectively. As shown in the table, A-subjects under the SP/WG setting respond to the cheap talk proposals by selecting the trust belief 138 times out of the 192 opportunities (72%) and A-subjects under the SP/SG setting respond to the cheap talk proposal by selecting the trust belief 86 times out of the 170 opportunities (51%). A test of proportions on A-subjects' responses to their M-partners' cheap talk proposals rejects (p<0.00) the null of no differences in A-subjects' behavior across the two settings.

Panel B of Table 9 shows the one-tailed test of proportions on A-subjects' beliefs under the two settings. The pair-wise comparison shows that there are significant differences for the trust and defensive beliefs (p<0.00) but not for the Nash belief (p<0.119). A-subjects under the SP/WG setting select the trust belief more frequently and A-subjects under the SP/SG setting select the defensive belief more frequently.

Panel C shows the frequencies and percentages of the fraud levels of M-subjects under the WS/WG and SP/SG settings. A chi-square test shows that M-subjects' choices differ significantly across the two settings (p<0.025). Panel D of Table 9 shows M-subjects do differ in their proportion of choices for the Nash and cheat choices (p<0.018), but not for the cooperate choices. M-subjects under the SP/WG setting select the cheat choice 62% of the time (126 times out of 203 opportunities) versus 51% (104 times out of 203 opportunities) under the WP/SG setting. The 11% difference represents the change in M-subjects' fraud level caused by the group pressure on A-subjects. Thus, under the SP/SG setting, A-subjects are less trusting of their M-partners than under the SP/WG setting and this induces M-subjects to cheat less. This can also be seen by comparing Figures 4 and 6.


 

Table 9: Examination of H5 - Comparing the Strong Pair/Weak Group Setting
to the Strong Pair/Strong Group Setting (Regular Play Phase)

 

Panel A

             
 

H5(Null):

Are there differences between A-subjects' beliefs across the SP/WG and SP/SG settings?

 

A-subjects' beliefs

           
 

2 - test

 

Trust
f1A

Nash
f2A

Defensive
f3A

Total

Average beliefs

 
 

SP/WG

 

139 (68%)

22 (11%)

42 (21%)

203

1.52

 
 

SP/SG

 

97 (48%)

31 (15%)

75 (37%)

203

1.89

 
     

Pr(X2 )=

0.000

Conclude: Choices differ

   
                 
 

How do A-subjects' respond to M-subjects' proposal?

       
 

One-tailed test of proportions

f1A | M sent a Proposal

     
   

SP/WG

138/192 = 0.72

     
   

SP/SG

86/170 = 0.51

     
   

Z-score

4.16

     
   

Pr(Z Zc)

0.000

     
   

Conclude

Responses differ

     
                 
 

Panel B

             
 

H5(Group):

Are A-subjects less trusting under the SP/SG than under the SP/WG setting?

 
 

One-tailed test of proportions

Trust
f1A

Nash
f2A

Defensive
f3A

   
   

SP/WG

139/203 = 0.68

22/203 = 0.11

42/203 = 0.21

   
   

SP/SG

97/203 = 0.48

31/203 = 0.15

75/203 = 0.37

   
   

Z-score

4.12

1.18

3.51

   
   

Pr(Z Zc)

0.000

0.119

0.000

   
     

Conclude: Lower frequencies of trust choice

   
                 
 

Panel C

             
   

Are there differences between M-subjects' fraud levels under the SP/WG and SP/SG settings?

 

2 - test

 

Trust
f1A

Nash
f2A

Defensive
f3A

Total

Average fraud

 
 

SP/WG

 

49 (24%)

28 (14%)

126 (62%)

203

2.38

 
 

SP/SG

 

51 (25%)

48 (24%)

104 (51%)

203

2.26

 
     

Pr(X2 )=

0.025

Conclude: choices differ

   
                 
 

Panel D

             
   

Do M-subjects committed less fraud under SP/SG than under SP/WG?

 
 

One-tailed test of proportions

Cooperate
f1

Nash
f2

Cheat
f3

   
   

SP/WG

49/203 = 0.24

28/203 = 0.14

126/203 = 0.62

   
   

SP/SG

51/203 = 0.25

48/203 = 0.24

104/203 = 0.51

   
   

Z-score

0.12

2.42

2.10

   
   

Pr(Z Zc)

0.454

0.008

0.018

   
     

Conclude: higher frequency of cheat choices

   

Results for H6: Hypothesis comparing A-subjects' beliefs across the resolution and regular play phases

H6(null) predicts that A-subjects will not change their frequency of selecting the trust belief after observing M-subjects' choices. That is, the frequency of trust choices will be the same during the resolution phase as during the regular play phase. Table 4 summarizes the relevant data. During the resolution phase of WP/WG, A-subjects choose the trust belief 35% of the time (23 times out of 66 opportunities) versus 42% of the time (85 times out of 203 opportunities) for the regular play phase. This difference is significant using a one tail test of proportion (p<0.02). The differences across the resolution and regular play phases are also significant for SP/WG and SP/WG, (p<0.02) but not for the WP/SG setting. Thus, when A-subjects are under the strong group setting and M-subjects cannot engage in cheap action/talk, the information about the M-subjects' fraud choices does not change A-subjects' propensity to trust their M-partner. This suggests that A-subjects' strategies are relatively stable under this regime and that the information about M-subject choices does not materially change the strategies of A-subjects.

Summary of the results using subjects' average choices

The right-hand column of Table 4 shows the average beliefs of A-subjects and average fraud levels of M-subjects. The pair combinations of average beliefs and average fraud levels under the WP/WG, SP/WG, WP/SG, SP/SG settings are (1.82, 2.22), (1.52, 2.38), (2.19, 1.93), and (1.89, 2.26) respectively. These data are shown graphically in Figure 7 and confirm the findings discussed above. More importantly, M-subjects' fraud levels are always higher than A-subjects' beliefs, except under the WP/SG setting. Figure 8 plots the average pair combinations as ordered pairs. Average A- subjects' beliefs are plotted on the horizontal axis and average M-subjects' fraud levels are plotted on the vertical axis for the four settings. Note that under the SP/WG, WP/WG, and SP/SG settings M-subjects have higher average fraud levels than their A-partners' average beliefs (above the 45 degree line) indicating that A-subjects are overly trusting of their M-partners. However, under the WP/SG setting, the average level of M-subjects' fraud is below A-subjects' average belief (below the 45-degree line) indicating relative distrust by the A-subjects. Figure 8 shows that under the SP/WG setting, M-subjects have the highest average fraud level and A-subjects' have the lowest average belief of fraud (i.e., A-subjects are most trusting) compared to the other three setting. On the opposite extreme, under the WP/SG setting M-subjects have the lowest average fraud level and A-subjects' have the highest average belief of fraud (i.e., A-subjects are least trusting). In the middle are the WP/WG and SP/SG settings, where M-subjects have roughly the same level of average fraud and A-subjects have roughly the same level of average beliefs.

Figure 9 duplicates the data from Figure 8 for the regular play phase, but also include the data from the resolution phase. The data are ordered pairs of average subject choices, with lines beginning at average choice values for the regular play phase and ending at average choice values for the resolution phase. For example, the line for the SP/WG setting begins at the point comprised of the average belief of 1.52 and the average fraud of 2.38 for this setting. The line and arrow pointing down and to the right (stopping at 1.91, 1.73) represent the average choice pair for the resolution phase. Note that under the SP/WG, WP/WG, and SP/SG settings, the average beliefs increased, and average fraud levels decreased in the resolution phase. That is, after A-subjects observed M-subjects fraud levels for the regular play phase rounds, A-subjects became less trusting and M-subjects committed less fraud. However, under the WP/SG setting, the average belief increases slightly and the fraud increases considerably in the resolution phase.




VI. Conclusions

A primary role of independent auditing is to enhance the credibility of financial statements. In order for audits to generate credibility, auditors must represent the interests of external parties, not those of management. For the past 30 years policy makers have debated the extent to which auditors can provide high quality audits (Pitt and Birenbaum 1997; MacDonald 1999; United States Senate 1977). Some conditions identified as having the potential to reduce audit quality include (1) lowballing, which involves setting audit fees in early periods below the cost of the audit (Craswell and Francis 1999; DeAngelo 1981; Dye 1991), (2) the provision of management advisory services (Antle et al. 1997; Dopuch and King 1991), and (3) direct and indirect financial and family ties (Fardella et al. 2000; Wallman 1996). These conditions are argued to lower audit quality because they increase managers' leverage over auditors. However, there are counterbalancing forces that reduce auditors' incentives to misreport, such legal sanctions imposed by courts/regulators and market penalties associated with the loss of reputational capital. Thus, auditors face tradeoffs between economic rents from misreporting and the potential imposition of economic penalties for misreporting. The debate in the policy arena is typically over the strength of each of these forces (General Accounting Office 1996; Public Oversight Board Advisory Panel On Auditor Independence 1994).

As an alternative to economic analysis, some researchers believe that audit quality may be reduced due to psychological reasons. For example, Bazerman et al. (1997) argue that even honest auditors cannot conduct impartial audits under existing conditions due to self-serving biases. The purpose of my research is to investigate self-serving bias in an experimental environment that incorporates both economic and psychological issues. The approach of combining both psychological and economic factors has been suggested by a variety of authors, including Kachelmeier (1996a) and King (1991).

The experimental results show that a self-serving bias does arise under my setting, however, the bias disappears when A-subjects are formed into groups. Thus, the psychological based self-serving bias is neutralized by the psychological forces created by auditor-subjects operating in groups. This suggests that the conclusion drawn by Bazerman et al. (1997) has to be modified. Although self-serving bias can affect decision-making, as suggested by these authors, this bias can be mitigated or neutralized by group affiliation.

Several limitations of this research should be highlighted. First, in order to convert a theoretical model into an experimental setting, certain functions and parameter values must be selected. Although I use functions and parameters consistent with the assumptions of the theory, I do not know how sensitive my findings are to different experimental values. Second, the setting has a game-theoretic basis, and the results may not generalize to market or organizational settings. Third, I used student subjects for the experiment rather than experienced auditors and investors. This may not be a material shortcoming because previous research has shown that student subjects may be most appropriate for testing models that do not incorporate mundane realism (Ball and Ceck 1996). Lastly, the experiment is devoid of context, without mention of fraud, audit, or self-serving bias. As suggested by Haynes and Kachelmeier (1998), the context can play an important role in affecting subject behavior.

Future research could modify my setting to incorporate a more realistic context. One possibility relates to building on the research of Kadous, Kennedy, and Peecher (2000) to investigate how motivated reasoning might affect the strategies of auditor-subjects, especially when there are competing goals from the client and the auditor group members. A second avenue for future research is to investigate how different pair/group configurations can affect the results. For example, it would be interesting to investigate the effect of groups on self-serving bias when the group is formed following the procedures used in practice.


Footnotes

1 The psychology literature on self-serving bias has at least two branches. The branch followed by Bazerman et al. (1997) relates to judgment and decision-making. A second (and related) branch focuses on how individuals attribute success and failures to oneself and to others (Campbell and Sedidides 1999; Mullen and Riordan 1988). See Kaplan and Ruffle (1998;1999) for a discussion of various definitions of self-serving bias. See Lewellen, Park, and Ro (1996) for a discussion of self-serving bias in a financial accounting context.
2 Bazerman et al. (1997) draw their conclusions about the impossibility of auditor independence based on a number of research articles that found subjects who were assigned different roles, such as plaintiff or defendant, made different decisions on how a judge would decide a case. See Babcock and Lowenstein (1997) for a review of this research.
3 See Jensen (2000) for a discussion of conflicting accountability for auditors.
4 For other auditing models see Antle (1984), Beck, Frecka, and Solomon (1988), Bloomfield (1995), Dye (1991), and Fellingham and Newman (1985).
5 Examples of auditing research using experimental economics include Bloomfield (1997), Calegari, Schatzberg, and Sevcik (1998), Dopuch and King (1991), and Kachelmeier (1991).
6 In game-theoretic settings, "cheap talk" refers to a form of communication that is costless, nonbinding, nonverifiable, and payoff irrelevant. Crawford (1998) reviews experimental research on cheap talk.
7 Bamber and Bylinski (1982) and Solomon (1987) review auditing research dealing with groups.
8 In the field, auditors also have economic ties, thus making group affiliation more important in the field. I did not include economic factors in order to determine whether noneconomic factors alone can undo the self-serving bias.
9 For research in the area of incentives and decision making, see Bonner et al. (2000), Kennedy (1995), Libby and Lipe (1992), Luft (1994), and Sprinkle (2000).
10 This situation could arise because M is acting as an agent for the investor and X represents the amount of money that rightfully belongs to the investor but is currently held by the manager. The game is presented as a fraud issue, however, it could be characterized as a reporting decision and retain the same frictions.
11 I assume audit quality, q(f A) is an increasing function of f A and the cost function, C(q), is increasing, convex, and twice differentiable on q(f A).
12 The first choice corresponds to a von Stackelberg outcome, the second to a Nash outcome, and the third to an outcome that makes M-subjects indifferent to committing fraud or not. To simplify the model and to make A's reaction function more transparent in the experiment, I constraint A's optimal belief choice to equal M's fraud level. That is, I constrain A's reaction function as follows: f*A = f. This is accomplished by judicious selections of functional forms and parameters, as shown in Table 2.
13 The numbers calculated from the equations can differ slightly from those used in the experiment due to rounding. The rounding of probabilities is done so that subjects view probabilities with only two digits in order to simplify the presentation. The roundings do not change the predicted equilibrium.
14 Instructions are available upon request.
15 The decision not to inform A-subjects of the amount of M-subjects' sanction was done so that A-subjects could not infer M-subjects' fraud levels until the end of the regular play phase. The justification for this approach is that auditors in the field may not learn the client's monetary penalty when fraud is discovered.
16 However, there may be psychological reasons why this information may affect the decision-making of A-subjects.
17 This restricted information condition was implemented in order to create a fertile environment for self-serving biases to arise. An interesting question is whether auditors can be leader in a leader/follower game in practice, however this issue is beyond the scope of the current study.
18 The resolution phase has only six rounds (and the regular play has 18 or more) so that M-subjects are not motivated to use the regular play phase to form reputations and then cheat during the resolution phase. With only six rounds in the resolution phase, the economic return from investing in reputations during the regular play is lessened. M-subjects were informed of the number of rounds in the regular play and resolution phases. A-subjects did not know the number of rounds, but knew there were fewer rounds in the resolution phase than in the regular play phase.
19 There is a Chinese proverb that states "Listen not to vain words of empty tongue."
20 Under the WP/WG, SP/WG, and SP/SG settings, five pairs of subjects interacted for 19 rounds and six pairs interacted for 18 rounds during the regular play phase. This generates a total of 203 observations (5 x 19 + 6 x 18 = 203) for these three settings. Under the WP/SG setting, all eleven pairs had 18 rounds during the regular play phase, thus producing 198 observations (11 x 18 = 198).
21 In the resolution phase, all M- and A-subject pairs played for 6 rounds (6 x 11 = 66) except one pair under the WP/SG setting played only 4 rounds due to network problem.
22 The random action hypothesis (H1null) is rejected for all four settings.



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