Deception and Incentives How Dishonesty Undermines Effort Provision Part 2

4.5 What Drives the E¤ort Decline in the PF Condition? While Result 4 provides a rationale for the agents’second stage e¤ort response to feedback in the PF condition, it does not explain the decline of average …rst and second stage e¤ort in the PF condition. Result 6 shows that this decline can be attributed to the experience of lying behavior. Result 6 (deception undermines incentives): The decline in average e¤ort over time is strongly a¤ected by the agents’deception experiences. The more often an agent has been deceived in the past the more the agent reduces …rst and second stage e¤ort. As documented previously in Results 4 and 5, principals engage in untruthful “underreporting”of the absolute value of the output di¤erence and hence a sophisticated agent who is or has become aware of the principals’reporting strategy should respond to the messages accordingly by reducing second stage e¤ort more than he would have done if the feedback given to him was entirely truthful. Result 6 indeed shows that on average agents respond correctly to the manipulated information of principals. How did the agents …nd out whether they have been deceived by a principal? When an agent has been told repeatedly in the past rounds that the …rst stage output di¤erence is very low in absolute value he might come to suspect that principals reported untruthfully. In fact, according to responses of subjects in the post-experiment questionnaire such a very low …rst stage output di¤erence alerts agents that some principals may report untruthfully. When asked how they detected whether principals engaged in lying behavior agents spontaneously cited low absolute values of reported …rst stage output di¤erences as the most important measure (64% of agents). This intuition of agents is indeed correct since output di¤erences that are small in absolute value are more likely to come from a dishonest than an honest principal. We therefore construct a measure that adds up the occurrences of very low reported output di¤erences for each agent over previous rounds. This measure of past lying behavior is the lagged cumulative sum of the occurrence of low di¤erence reports (LOW DIFFERENCE ). We classi…ed any report of the …rst stage output di¤erence between 3 and 3 as a low di¤erence thus creating a binary variable.12 About 38% of all reports over all the rounds of the experiment fall into this range which also includes the modal report (2). The lagged cumulative sum of 6. 12 We also conducted robustness checks with di¤erent cut-o¤ levels such as [ 1; 1] and [ 5; 5] as well as robustness checks using di¤erent measures of deception occurrences such as the sum of the absolute values of past output di¤erences. The results are qualitatively similar. 25 the number of low reported output di¤erences captures the idea that agents who have more reason to believe that they have been deceived in the past are more likely to discount feedback information in the current round. The number of agents who experience such a low output di¤erence increases over time. Whereas at the start of round 2 only 18 out of 64 contestants have received very low feedback about the output di¤erence, in round 15 there are 61 contestants who have previously received a very low output di¤erence report. We investigate whether this measure of past lying behavior in‡uences second stage e¤ort choice by running the regressions reported in Table 7. The experience of past lying behavior leads contestants to exert less e¤ort in stage 2 as speci…cations (2), (3) and (4) reveal. In all these speci…cations the coe¢ cient on the lagged cumulative sum of low output di¤erence report occurrences is negative and statistically signi…cant and the e¤ort response to information feedback is now even more pronounced than in the models for the PF condition presented in Table 3. On average, for any low reported output di¤erence that a contestant has received from a principal in the past he reduces e¤ort by 0:99 as shown in column (2). Note that the coe¢ cient on the ROUND variable which is signi…cant in column (1), is no longer signi…cant whenever we control for past lying experiences. In fact, when we control for past lying behavior the coe¢ cient for the round variable becomes even positive (though insigni…cant). Thus the decline in second stage e¤ort over time is not simply a time trend but it seems to be driven by the experience of past lying behavior. Insert Table 7 here. Next, we analyze whether similar e¤ects can be found for …rst stage e¤ort. According to the model in Section 2 the information agents receive at the end of the …rst stage is only relevant for second stage e¤ort. First-stage e¤ort should be the same regardless of how much information is transmitted; therefore it should be the same across all three conditions (NF, TF and PF) and constant over time. As Result 3b showed this is in fact the case for the …rst stage e¤ort in the NF and TF condition, where average …rst stage e¤orts were statistically indistinguishable and constant over time despite the di¤erences in information release before the beginning of the second stage. As before, we investigate whether the e¤ort decline in the PF condition is a reaction to the increasing awareness of agents that principals are lying. We run OLS regressions of …rst stage e¤ort on the past lying measure (LOW DIFFERENCE ) and the number of rounds shown in Table 8. On average, for any low reported output di¤erence that a contestant has received from a principal in the past he reduces e¤ort by 1:07 as shown in column (2). As in our analysis of second stage e¤ort, the coe¢ cient on the ROUND variable which is signi…cant in column (1) is 26 no longer signi…cant. Finally, we note that our results are robust to di¤erent cut-o¤ levels for the classi…cation of low di¤erence reports. Model (3) in Table 8 also reports regression results for the symmetric cut-o¤ level of [ 1; 1]. Insert Table 8 here. We also investigated whether there is a similar e¤ect on …rst and second stage e¤ort in the TF condition where feedback is truthful. As expected, there is no signi…cant evidence of such an e¤ect regardless of the cut-o¤ we choose for classifying a low di¤erence. Thus the behavior documented in Tables 7 and 8 is due to agents anticipating that principals are lying rather than the consequence of a simple learning e¤ect for second stage e¤ort. 5 Interpretation The previous section shows that when there is either no feedback (NF condition) or completely truthful feedback (TF condition) the theoretical model proposed in Section 2 works remarkably well. The experimental evidence largely con…rms the predictions of the model; the agents e¤ort is decreasing in j j and the average e¤ort in both stages of the NF condition and the …rst stage of the TF condition are very similar. In addition, the average e¤ort in the second stage of the TF condition is smaller than e¤ort in the NF condition. Note that this prediction relies on a subtle aspect of the model (the convexity of the marginal cost function) and we …nd it quite remarkable that the data support it. In contrast, when information can be manipulated and feedback is given by self-interested principals, the theoretical model is no longer supported by the experimental data. Contrary to the theoretical predictions, communication by principals is at least partially informative and agents strongly respond to the messages sent by principals. Furthermore, agents signi…cantly reduce their average e¤ort in the …rst and the second stage if they have experienced lies in the past. It seems that the principals’deceitful behavior thoroughly undermines e¤ort provision. These experimental results naturally lead to us to ask a new set of questions: Can we explain the failure of the cheap talk hypothesis with a simple and parsimonious theoretical model? Are other theories equally successful at explaining the theoretical results about principals’reporting behavior and agents’e¤ort choice? In this section we interpret our experimental …ndings in the light of the failure of the cheap talk hypothesis, the evidence gathered from the previously discussed results and a simple and parsimonious model of lying aversion, which explains many of the puzzling features documented previously. Furthermore, we show that social preference theories based on motives of altruism, 27 reciprocity and inequity aversion cannot explain key observations such as the informativeness of the principals’messages. The lying aversion model is developed in greater detail in Appendix B, and Appendix C contains a more detailed analysis of the predictions of social preference theories. Before we address the question of how the existence of lying-averse subjects can account for many observations in the PF condition, it is worthwhile to stress that lying aversion cannot play a role in an environment in which lying is impossible. Thus, lying aversion obviously cannot a¤ect behavior in the NF and TF treatment, implying that the predictions of the model described in Section 2 apply. Therefore, the fact that behavior in the NF and TF condition largely meets the predictions of the model in Section 2 is perfectly consistent with the assumptions of lying aversion. 5.1 Principals’Reporting Behavior We begin our analysis with the reporting behavior of principals. In our baseline theoretical model of Section 2 principals would report whichever output di¤erence maximized an agent’s e¤ort for a given belief of the agent; principals should therefore deviate from reporting the truth whenever it is in their interest to do so. Consider the following situation in which the principal holds …xed beliefs such that an agent will exert higher e¤ort for a reported output di¤erence that is lower in absolute value. Clearly, this is a reasonable assumption given the observed average e¤ort response in the PF condition shown in Figure 2. Now, consider the case of heterogenous principals who have di¤erent preferences for truthtelling because they su¤er di¤erent disutility when they report untruthfully. When deciding what message ^ i to send to agent i they have to weigh the bene…ts against the disutility of lying. When agents exert higher e¤ort for a reported output di¤erence that is lower in absolute value then the bene…ts of lying come from “underreporting” the output di¤erence. However, since such “underreporting” also involves costs when the principal is averse to lying, she may often choose to keep lying disutility low by not lying maximally, i.e. she will not report an output di¤erence very close or equal to zero, or even avoid lying costs altogether by reporting truthfully. When principals have a preference for reporting truthfully then the actual output di¤erence matters for the principal’s reporting behavior. This is one of the key predictions (Theoretical Result 1) of the lying aversion model presented in Appendix B which ‡eshes out the above argument more formally and in more detail. The rationale for lying as a cost-bene…t decision is further supported by the evidence summarized in Result 5 where we show that reporting behavior is driven by the gains from lying. Clearly, the fact that there is some truthful reporting and the reports in general depend on the actual realization of the output di¤erence is what makes communication at least partially informative. 28 Theoretical Result 1 also shows that each reported …rst stage output di¤erence should be either equal to or smaller in absolute value than the actual output di¤erence. This e¤ect is due to the e¤ort-increasing e¤ects for “underreporting”described above. Again, the theoretical result is strongly supported in our data where more than 95% of all reports are either truthful (i.e., equal to the actual output di¤erence) or smaller in absolute value than the actual output di¤erence. While our model of lying aversion can explain the principals’ behavior, theories of social preference based on motives of altruism, reciprocity or inequity aversion fail to do so. We show this in more detail in Appendix C and provide some intuition here. When the principal has altruistic motives and cares equally about the two agents, she is indi¤erent which agent wins the tournament. The principal’s private reporting decision to an agent is therefore only a¤ected by second stage e¤ort (multiplied by ) chosen by the agent and the associated cost of e¤ort. Since second stage e¤ort only depends on the reported output di¤erence, but not the actual output di¤erence, which is not observed by the agent, the optimal report of an altruistic principal is independent of the actual …rst stage output di¤erence. As a result, we should not observe any systematic relationship between actual and reported output di¤erences whereas in the data we clearly do. The same argument applies to an inequity-averse principal or a principal who responds reciprocally to the …rst stage output levels by putting more weight on the welfare of the agent with a higher output. It is also worthwhile to point out that the concept of quantal response equilibrium does not seem to be able to explain the dependence of the principals’messages on the true output di¤erences. The reason for this is that the quantal response approach assumes that players play noisy best replies, i.e., they tend to make mistakes and these mistakes are more likely if the costs of a mistake are low. In our PF condition, the agents’e¤ort response to a reported output di¤erence is given by the graph displayed in Figure 2. A self-interested principal who plays a noisy best reply to this e¤ort response should always report the output di¤erence that maximizes her payo¤ with the highest probability but –due to the noise in the best reply –she will also report neighboring output di¤erences with positive probability. Thus, this approach can explain why principals will not always tell the truth but it cannot explain why the principals’ feedback information depends on the true output di¤erence. As documented in Result 5 there is heterogeneity in reporting behavior across principals; some principals lie more and more often than others. In our model of lying aversion this di¤erence in preferences is captured by a lying aversion parameter which determines the strength of lying aversion and varies across principals. Consider two principals with di¤erent levels of lying aversion who observe the same …rst stage output di¤erence and decide how to report to the agents. Reporting untruthfully generates the same bene…ts for the two principals, however for the same deviation from the truth the more lying-averse principal su¤ers greater disutility than 29 her less scrupulous counterpart. As a result, more lying-averse principals will lie less in equilibrium. This prediction is also apparent in our experimental data where principals with weak Machiavellian personality traits lie considerably less often than principals with intermediate or strong Machiavellian traits as shown in Result 5 and Table 6. 5.2 Agent E¤ort Response Turning our focus to the e¤ort choice of agents it seems that the main reason why the baseline model fails in the PF condition is the informative content of principals’ messages. In fact, once we recognize that communication is informative key aspects of agents’behavior in the PF condition make sense. The previous section showed that all principals will either “underreport”or report truthfully, but will never report untruthfully when they do not gain from doing so. As a result, any agent should expect that the actual …rst stage output di¤erence relevant for his second stage e¤ort decision is larger in absolute value than the …rst stage output di¤erence ^ i reported to him. As we showed in our discussion of Result 4, on average the actual …rst stage output di¤erence is about twice as large as the reported one and more than 95% of all reports are either truthful (i.e., equal to the actual output di¤erence) or smaller in absolute value than the actual output di¤erence. Hence, for any given reported output di¤erence a rational agent should exert less e¤ort than in the case where feedback is completely truthful. This is exactly the behavior we derive in Theoretical Result 2 in Appendix B: for a given report agents are predicted to exert less e¤ort in the PF condition than in the TF condition. While the experimental data strongly support the qualitative predictions of our model, we are also interested in how close actual second stage e¤ort choices are to optimal e¤ort choices. An optimal e¤ort choice requires agents to perform the correct inference from a message sent by the principal as well as making an appropriate e¤ort choice. In our discussion of the TF condition we already showed that agents e¤ort choices are close to optimal when all communication is truthful and there is no complicated inference process. Consider now the case of a rational agent in the PF condition. Since there is heterogeneity in lying behavior among principals, when receiving a report about the …rst stage output di¤erence ^ i the agent does not know exactly what the actual output di¤erence is. However, he knows the distribution of the actual output di¤erence. In other words, the agent knows the posterior distribution of following a message ^ i which is given by Pr( j ^ i ). Consequently, he also knows his conditional probability of winning the tournament which is given by Pr(ei2 ej2 + + "2 > 0 j ^ i ): Given this posterior distribution the agent chooses his second stage e¤ort level appropriately. We can further back out the posterior distribution of given ^ i from our experimental data 30 using Kernel estimation and then compute the optimal response for a given ^ i . A comparison of these optimal e¤ort choices with actual e¤ort choices reveals that the di¤erence between the two is not statistically signi…cant at the 10% level (t-test, p-value 0.16).13 5.3 Dynamics We are also interested in understanding the dynamics of e¤ort choices in the PF condition. As shown by Result 6 contestants who receive a higher number of low output di¤erence reports in previous periods, adjust their second stage e¤ort response downwards. Our model of lying aversion (Theoretical Result 3) explains this behavior by a simple updating process about the relative proportions of high and low lying-averse principals on behalf of the agents. If agents are uncertain about the exact proportions of honest and dishonest principals, they will update their beliefs about the relative proportions of honest (more lying-averse) and dishonest (less lyingaverse) principals according to the messages they have received in the past. The interaction with more dishonest principals which entails repeatedly observing an output di¤erence that is particularly low in absolute value, will then lead agents to rationally expect that the actual proportion of dishonest principals is high. In turn, when agents believe that the proportion of lying principals is high they will adjust their e¤ort response downward by treating any message they receive more skeptically. By reporting output di¤erences that are low in absolute value a principal achieves a higher payo¤ for himself, but also undermines the collective credibility of principals which leads to a changed second stage e¤ort response in later periods. There is one feature in our data that our model, which departs from the standard model only by introducing rational lying aversion among the principals, cannot readily explain. In Result 3 we show that …rst stage average e¤ort strongly declines over time. However, rational and self-interested agents should not change their …rst stage e¤orts regardless of how much the principals underreport the true output di¤erences (see Section 2). The rational response of a self-interested agent to underreporting is to discount the principals’ messages and to choose the second stage e¤ort accordingly. Yet, in fact the principals’ underreporting of the truth seems to more thoroughly undermine the agents’willingness to provide e¤ort by reducing …rst stage performance. It is possible to account for this phenomenon if one extends the notion of lying aversion such that lying aversion not only incorporates the psychic costs of lying but also the resistance of the victim of the lie. The evidence in Sanchez-Pages & Vorsatz (2007) and Brandts & Charness (2003) indicates the existence of subjects that are willing to punish We assumed that following a message ^ i player i knows the exact equilibrium e¤ort of his opponent. However, we also performed the same analysis for the case where following a message ^ i player i only knows the distribution of e¤orts of his opponent. As before, the di¤erence between actual and optimal behavior is not statistically signi…cant at the 10% level. 13 31 lying per se. These authors show that the same payo¤ consequences trigger quite di¤erent punishment behaviors depending on whether the payo¤s have been generated by a lie. Subjects are much more willing to punish an opponent for generating a payo¤ allocation if the opponents’ behavior is based on a lie. In our setting, the anticipation of being the victim of a lie could have induced the agents to decrease also their …rst stage e¤ort. Moreover, agents who have more reason to believe that the principal will lie, i.e., those agents who experienced a higher number of small output reports in the past, also have more reason to respond with a lower …rst stage e¤ort. 6 Conclusion In this paper we have shown that deceptive information by the principals eventually undermines the e¤ectiveness of performance incentives. The principals initially bene…t from deceiving the agents because the underreporting of output di¤erences induces agents to work harder compared to a truthful output report. However, despite massive underreporting the average e¤ort in the second stage of the tournament eventually falls below the e¤ort in the No Feedback treatment and the Truthful Feedback treatment because the agents strongly discount the principals’ feedback information. Moreover, the agents not only reduce their e¤ort in direct response to the principals’feedback but they also show a strong decline in …rst stage e¤ort levels indicating a pervasively negative e¤ect of deception on tournament incentives. This decline in average e¤ort levels seems to be driven by agents’previous experiences of deception. In order to assess these results it is important to keep in mind that the agents knew that the winner of the tournament was determined objectively by the total output di¤erence after stage two. Therefore, the principals could not engage in favoritism by falsely proclaiming one player the winner of the tournament, nor did the principals have incentives to do so in our setting. In our view, this renders the fact that the agents average …rst and second stage e¤ort in the PF condition falls below the e¤ort in the No Feedback and the Truthful Feedback condition all the more remarkable. This …nding suggests that for an organization it may be better to provide no feedback to the agents in promotion tournaments unless the principal can commit to provide fully truthful feedback. In view of our results it is interesting that the organizational behavior literature documents that performance feedback is often uninformative and therefore largely disregarded by workers (Beer (1987), Gibbs (1991)) unless managers are scrutinized on and held accountable for their appraisal of subordinates (Lockenecker, Sims and Gioia 1987). Our data suggest that the detrimental impact of the principals’feedback on average e¤ort is due to the deceptive nature of this feedback. However, the data also suggest that the principals’ imperfect lying behavior, i.e., the fact that the principals’messages are informative about the true output di¤erences, also played a role. If the principals’ feedback had been completely 32 unreliable the agents would have had an incentive to behave as if they had been given no information. Recall that according to the chosen experimental parameters e¤ort in the NF condition is predicted to be (and actually turned out to be) even higher than in the TF condition, that is, if the agents had completely disregarded the principals’feedback we should not have observed a detrimental e¤ect of feedback information on incentives. We regard it, however, as an open question whether agents would indeed not respond at all to completely deceptive (i.e., completely uninformative) feedback by the principals. It is hard to believe that extreme forms of intentional lying do not provoke some e¤ect on agents’ e¤ort. In fact, the strong decline in …rst stage e¤ort levels in our setting is consistent with the idea that people dislike being the victim of a lie. In view of our results we thus believe that it is worthwhile to study the psychological forces associated with lying and the consequences of these forces for contracts and incentives. For example, in our setting, principals who anticipate incurring costs of lying aversion, may shy away from giving any form of feedback if they are not forced to do so. Furthermore, if the past reporting behavior of principals is observable they may have an incentive to develop a reputation for truth-telling. In general, a large class of contracting problems is characterized by lying incentives, and a better understanding of the motivational forces associated with lying or with being the victim of a lie may enhance our understanding of these problems. 33 A A.1 Omitted Proofs First Stage E¤ort in the TF Condition When feedback is truthful at the beginning of the …rst stage agent i chooses ei1 to maximize his utility h i U i = p + (P p)G(ei1 + eT2 F;i ej1 eT2 F;j ) c(ei1 ) E c(eT2 F;i ) : De…ne the noise di¤erence t as t "it "jt then ej1 + = ei1 1: Since the noise di¤erences are independently (normally) distributed we can rewrite the principal’s utility in the following way h i h i U i = p + (P p)E 1 F (ei1 + eT2 F;i ej1 eT2 F;j + 1 ) c(ei1 ) E 1 c(eT2 F;i ) : To obtain the …rst order conditions we di¤erentiate this expression with respect to ei1 . The …rst order conditions are given by h i c0 (ei1 ) = (P p)E 1 f (ei1 + eT2 F;i ej1 eT2 F;j + 1 ) (A1) # " # " T F;i T F;i de de 2 2 E 1 c0 eT2 F;i +(P p)E 1 f ei1 + eT2 F;i ej1 eT2 F;j + 1 dei1 dei1 " # T F;j de (P p)E 1 f (ei1 + eT2 F;i ej1 eT2 F;j + 1 ) 2 i : de1 The …rst line of equation (A1) captures the direct e¤ect of ei1 , the second line represents the e¤ect of ei1 on eT2 F;i , and the third line is the strategic e¤ect of ei1 on eT2 F;j . The three lines correspond to the three di¤erent e¤ects discussed in the main part of the paper. We now show that the second and the third line are zero. Denote the second line of (A1) by K. We note the symmetry of the second-period equilibrium e¤ort levels, eT2 F;i = eT2 F;j and use the law of iterated expectations to rewrite the second line in the following way " # h i deT F;i ( ) 2 K = E E 1 (P p)f ( ) c0 (eT2 F;i ( )) j dei1 h i deT2 F;i ( ) 0 T F;i = E E 1 (P p)f ( ) c (e2 ( )) j dei1 = 0 34 since p)f ( ) = c0 (eT2 F;i ( )) (P which is the …rst order condition of the second stage e¤ort choice given in equation (4). The strategic e¤ect given by the third line of (A1) is zero as well in a symmetric equilibrium. Denote the term in the third line of (A1) by S. First, there is a …rst stage equilibrium that is symmetric in e¤ort levels, i.e., eT1 F;i = eT1 F;j eT1 F and therefore = 1. Second, the second stage e¤ort equilibrium is symmetric eT2 F;i ( ) = eT2 F;j ( ) = eT2 F ( ) and eT2 F ( ) is symmetric in around 0, i.e., eT2 F ( ) = eT2 F ( ): Substituting these expressions into the third line we obtain " S = (P p)E f (ei1 + eT2 F;i 1 = (P p)E 1 = (P p)E 1 " ej1 deT F;j ( 1 ) f ( 1) 2 d 1 eT2 F;j # deT F;j ( ) + 1) 2 i de1 # f ( 1 )eT2 F 0 ( 1 ) where deT2 F ( 1 ) : d 1 From the properties of the density function we know that f is symmetric in 1 around 0. Furthermore, from equation (5) characterizing equilibrium second stage stage e¤ort we know that eT2 F ( 1 ) is symmetric in 1 around 0 and that it achieves a maximum at 1 = 0, so eT2 F 0 ( 1 ) f ( 1) = f ( 1) eT2 F ( 1 ) = eT2 F ( eT2 F 0 ( 1 ) = eT2 F 0 (0) = 0: 35 eT2 F 0 ( 1) 1) Rewriting the expression for S we have Z 1 f ( 1 )eT2 F 0 ( 1 )f ( 1 )d 1 S = (P p) 1 Z 1 Z 0 2 TF0 = (P p) [f ( 1 )] e2 ( 1 )d 1 + [f ( 1 )]2 eT2 F 0 ( 1 )d 1 1 0 Z 1 Z 0 2 TF0 [f ( 1 )]2 eT2 F 0 ( 1 )d [f ( 1 )] e2 ( 1 )d 1 + = (P p) 1 Z 1 0 Z 1 [f ( 1 )]2 eT2 F 0 ( 1 )d 1 + [f ( 1 )]2 eT2 F 0 ( 1 )d 1 = (P p) 0 1 0 = 0: The …rst order condition therefore simpli…es to c0 (eT1 F ) = (P A.2 p)g(0): Expected Second Stage E¤ort in the TF Condition In equilibrium, the expected e¤ort in the second stage in the TF condition E[eT2 F ] where feedback is truthful, is lower (higher) than e¤ort in the NF condition eN F where no feedback is given, if the marginal cost function c0 is convex (concave). Since the noise di¤erences are independently (normally) distributed equation (2) can be rewritten in the following way c0 (eN F ) = (P = (P p)g(0) p)E 1 [f ( 1 )] = E 1 [(P p)f ( )] = E 1 [c0 (eT2 F ( ))] where we used the fact that eT1 F;i = eT1 F;j eT1 F (and therefore = 1 ) as well as equation (4). Using Jensen’s inequality we can provide a ranking of eT2 F ( ) which is a random variable and eN F which is a constant. If c0 is convex, then Jensen’s inequality implies c0 (eN F ) = E 1 [c0 (eT2 F ( ))] c0 (E 1 [eT2 F ( )]) and hence eN F E[eT2 F ] since c0 is increasing. Clearly, if c0 is concave the reverse inequalities hold. If the cost function is quadratic, then marginal cost is linear and eN F = E[eT2 F ]. B A Model of Communication with Lying Aversion In this appendix we present a model that provides the theoretical underpinnings for our discussion and interpretation of results in Section 5. 36 There is some evidence from psychological and economic research that individuals are averse to lying even when it is in their interest to do so (Gneezy (2005), Hurkens & Kartik (2008)). Consider the following change in the principal’s payo¤ function UP = B A B xA 1 + x1 + x2 + x2 P p l X i=A;B where h j ^ i h j^i j (B1) 0) and convex (h00 0) in the absolute value of the di¤erence between the reported output di¤erence ^ i and the actual output j is a lying term that is increasing (h0 di¤erence . The principal su¤ers disutility when she reports an output di¤erence that di¤ers from the truth and this disutility is increasing in the di¤erence between the reported value and the truth. Note that l is a positive constant that may vary across principals. The higher is l the stronger is the principal’s aversion to lying. B.1 Communication Equilibrium We now characterize a communication equilibrium with naive senders. When considering what message ^ i to send to agent i the principal has to weigh the bene…ts against the disutility of lying. Naive senders believe that agents do not anticipate that the sender will not report truthfully. In other words, they believe that the agents will not adjust their e¤ort behavior in response to the principals’lies. For a given taking …rst order conditions for a report to agent i we …nd that principal’s utility varies with ^ i in the following way @eP2 F;i @U P = @ ^i @ ^i lh0 j ^ i j : (B2) The …rst term on the left-hand side of the equation is the marginal bene…t of lying whereas the second term gives the marginal cost of lying. In contrast to our model without lying disutility the optimal message now depends on . Furthermore, note that eP2 F;i ( ) is a function that has the shape of a normal density. For values of close to zero second stage e¤ort eP2 F;i is not very responsive to changes in , that is, the marginal bene…t of lying is very small in that range. Hence, if the marginal cost of lying is strictly increasing (h0 > 0), for l large enough and close enough to zero the principal’s i ^ optimal report is a corner solution, that is the principal reports the truth. For a principal with lying aversion l denote this cuto¤ for j j below which truthful reporting occurs by (l), in other words, if j j < (l) then ^i ( ) = : 37 Note that this cuto¤ (l) is increasing in l. Clearly, as the principal’s lying aversion goes to zero, this cuto¤ will go to zero, i.e., (0) = 0, so a principal who is not lying-averse will lie maximally (report 0) all of the time. The marginal bene…t of lying increases as j j increases and may eventually overwhelm the disutility of lying. This is because as j j increases the slope of eP2 F;i ( ) may become steeper than the slope of the lying term. Lying, however, is not maximal since the optimal message ^ i is not equal to 0, but is given by the report that balances the marginal bene…t and marginal cost of lying, @eP2 F;i j : (B3) = lh0 j ^ i i ^ @ One should also note that since the second stage e¤ort has the same shape as a normal density, which is ‡at around the mean of 0 and also ‡at in the tails, the marginal bene…t to lying decreases again as j j increases above 40. Thus, at some point given by (l) it will no longer be pro…table at all for the principal to lie. This feature of our model is unobservable in our data since even very honest principals (with high l) would report truthfully only for very large values of j j. For example, according to our model a very honest principal (such as the principal shown in right panel of Figure 6) who reports truthfully for j j < 20 (so (l) = 20) should also report truthfully for j j > 64 (so (l) = 64). In our data, this principal is never put in such a situation. In fact, when calculating the principal-speci…c cuto¤s (l) from our data and the implied cuto¤s (l) we …nd that extreme realizations of j j > (l) constitute less than 0.5% of our data. We therefore ignore this slightly peculiar feature of our model. In summary, this gives our …rst theoretical result. Theoretical Result 1: If the principals believe that agents will naively follow their report, for small values of j j < (l) the principal’s optimal reporting strategy ^ i ( ) for a given is to report truthfully, i.e. ^ i ( ) = if j j < (l) and it is characterized by the …rst order condition in (B3) for intermediate values, (l) < j j < (l). Furthermore, the reported output di¤erence is always lower than the true output di¤erence, j ^ i j j j: Principals with lower l lie more. If lying aversion is su¢ ciently large, principals always report the truth ^ i ( ) = and principals always lie maximally ^ i ( ) = 0 if lying aversion is su¢ ciently small. 38 B.2 E¤ort Choice Consider now the agents’e¤ort choice. As mentioned before, there is heterogeneity with respect to lying aversion among the principals and agents do not know with which principal they are matched. The agents therefore do not know each principal’s aversion to lying given by the parameter l and the resulting cuto¤ (l) above which lying occurs. A report ^ i may be truthful if it is coming from a truthful principal with high l or it may be a lie sent by a principal with low l. However, from Theoretical Result 1 we know that j ^ ij j j since principals would never want to tell a lie if it decreases their pecuniary payo¤. Realizing that principals have an incentive to underreport agents should adjust their response accordingly. This gives us our second theoretical result. Theoretical Result 2: For a given reported …rst stage output di¤erence ^ i second stage e¤ort in the PF condition is lower than in the TF condition, that is we have eP2 F;i ^ i eT2 F;i ^ i 8^i where eP2 F;i ^ i and eT2 F;i ^ i represent the second stage e¤orts in the PF condition and in the TF condition, respectively. B.3 Dynamics We now turn to a theoretical analysis of the dynamics observed in the data. Consider the following simpli…cation. Assume that the principals are independently drawn from a population of two types of senders. With probability the sender has low lying aversion l > 0, otherwise (probability 1 ) the sender has high lying aversion with l > l. Contestants are initially uncertain about the exact proportion of sender types, but hold a correct prior m where E[ ] = m: The agents update their beliefs about to form a posterior ^ i according to information obtained while playing in the experiment. As shown before, for a given output di¤erence a principal with low lying aversion will lie more than a principal with high lying aversion. Thus, a reported output di¤erence that is particularly low in absolute value, i.e. j ^ i j < k where k is positive but small, increases the probability that it was sent by a principal with low lying aversion. More importantly though, in this setting where the exact probability is unknown (in contrast to where it is known with certainty) receiving a low output di¤erence message does 39 not only provide information about the type of the sender but also provides information about the actual proportions of low- and high-lying-averse principals. Ceteris paribus, a contestant who has received a low output di¤erence message j ^ i j < k in previous rounds will now hold a higher posterior ^ i than a contestant who has not received such a message. Furthermore, a contestant with a higher posterior ^ i anticipates there to be more lying (due to a higher proportion of lying principals) and will therefore adapt his e¤ort response accordingly. In particular, we have eP2 F;i ^ i ; ^ i0 eP2 F;i ^ i ; ^ i 8 ^ i and ^ i ^ i0 : This yields our third theoretical result which captures the dynamic e¤ort response e¤ects documented in Result 6. Theoretical Result 3: For a given reported output di¤erence contestants who in previous rounds have received low output di¤erence reports such that j ^ i j < k where k > 0 but small should exert lower second stage e¤ort levels than contestants who have not received such low output di¤erences. C Social Preference Theories In Appendix B we outlined a simple model of lying aversion that is able to explain the failure of the cheap talk hypothesis. In this appendix we consider other theories that depart from sel…sh maximization of monetary gains. We show, in particular, that social preference theories based on motives of altruism, reciprocity and inequity aversion cannot explain key features of our experimental results such as the dependence of ^ i on . C.1 Altruism Consider the case of an altruistic principal with the following objective function X B A B U P = xA + x + x + x P p + Ui 1 1 2 2 i=A;B where re‡ects how much the principal cares about the payo¤s of the agents. We can rewrite the objective function in the following way P U = xA 1 + xB 1 + xA 2 + xB 2 (1 )(P + p) 2 X X c(eit ): t=1 i=A;B In contrast to the …rst stage e¤ort choices ei1 which do not depend on the principal’s messages ^ i , the second stage e¤ort eP2 F;i ( ^ i ) is in‡uenced by the principal’s message. However, since 40 the agent never observes the actual output di¤erence , the second stage e¤ort eP2 F;i ( ^ i ) does not depend on . The interior solution for the message to agent i is given by the …rst order condition @U P @eP2 F;i c0 (ei2 ) = 0 for i = A; B: (C1) = @ ^i @ ^i Note, that this expression does not depend on and hence for every value of the principal should report the same value of ^ i . This is clearly refuted by the data since for almost all principals there is a signi…cantly positive relationship between and ^ i . C.2 Reciprocal Altruism Consider now the case of a reciprocally altruistic principal. Since the interim winner of a tournament has produced more output for the principal the principal might care more about the interim winner’s payo¤ than the interim loser’s. When agent A is ahead, that is 0, then the principal attaches a weight to agent A’s and a weight to agent B’s payo¤ and vice versa when < 0, where . This captures the e¤ect of reciprocity. Since the setting is symmetric without loss of generality, let 0 so that the principal feels more altruistic to agent A than to agent B. The principal’s objective function is therefore given by B A B U P = xA P p + U A + U B: 1 + x1 + x2 + x2 The …rst order conditions for ^ i are @eP2 F;A h @U P = +( @ ^A @ ^A @eP2 F;B h @U P = ( @ ^B @ ^B )(P p)f (eP2 F;A eP2 F;B + ) )(P p)f (eP2 F;A eP2 F;B + ) @eP F;B Multiplying the …rst condition by @2^ B and the second condition by two equations we obtain after simpli…cation 2 c0 (^ eA 2) i c0 (eA ) =0 2 i c0 (eB ) = 0: 2 F;A @eP 2 ^ @ A and adding these c0 (^ eB 2) = 0 (C2) which has to hold for interior solutions of ^ i regardless of the value of . As in our previous analysis this expression does not depend on and hence for every value of the principal i should report the same values of ^ which is refuted by the data. C.3 Inequity Aversion Consider the case of an inequity-averse principal with preferences given by X X P UP = P max U i ;0 max P U i ; 0 2 i=A;B 2 i=A;B 41 where P B A B xA 1 + x1 + x2 + x2 = P p and > 0. We analyze three cases here where the principal’s pro…t is either greater or smaller than the payo¤ of both agents, or between the two. As we will see, inequity aversion cannot explain the reporting behavior of principals in any of the three cases. First, if P maxfU A ; U B g then the principal’s utility is given by UP = P 2 X max P U i; 0 i=A;B and hence the same conclusions hold as for the case of simple altruism where the state of nature does not in‡uence the principal’s choice of message. Second, if P minfU A ; U B g then preferences are given by UP = P 2 X max U i P ;0 : i=A;B In this case the principal behaves spitefully but otherwise the same argument as in the …rst case applies, i.e., the message should not depend on . Third, consider the case where P lies between the two agents, e.g. U A UP U B . In this case, the principal’s …rst order conditions are given by @U P @eP2 F;A = @ ^A @ ^A @U P @eP2 F;B = @ ^B @ ^B 1+ 1+ + 2 2 + (P 2 p)f (eP2 F;A eP2 F;B + ) + (P 2 p)f (eP2 F;A eP2 F;B + )+ 2 2 c0 (eP2 F;A ) = 0 c0 (eP2 F;B ) = 0 which we can add and simplify to obtain 2 1+ 2 + 2 c0 (eP2 F;A ) 2 c0 (eP2 F;B ) = 0: As in the previous cases this condition does not depend on should not depend on the …rst stage output di¤erence . 42 (C3) and hence the optimal message