TWO ESSAYS ON INVESTORS PERCEPTIONS ABOUT MANAGEMENT DISCLOSURES

Transcription

1 TWO ESSAYS ON INVESTORS PERCEPTIONS ABOUT MANAGEMENT DISCLOSURES A Dissertation Presented to the Faulty of the Graduate Shool of Cornell University In Partial Fulfillent of the Requireents for the Degree of Dotor of Philosophy by Hailan Zhou August 007

2 007 Hailan Zhou

3 TWO ESSAYS ON INVESTORS PERCEPTIONS ABOUT MANAGEMENT DISCLOSURES Hailan Zhou, Ph. D. Cornell University 007 In this dissertation, I desribe two studies related to investors pereptions about anageent dislosures. In the first study, I use a variant of Dye and Sridhar (004) to show analytially that investor unertainty about anagers reporting inentives to anipulate inforation redues the degree to whih aounting reports should weight anipulable inforation. I also predit and show experientally that greater weight on anipulable inforation in the fae of inentive unertainty hars investor welfare ore than predited by equilibriu analyses, by hindering anagers and investors ability to predit one another s strategies. The resulting deviations fro equilibriu ause the pereived and atual value-relevane of finanial reports to vary over tie in preditable (and testable) ways. In the seond study, I report an experient that exaines how investor affet ight influene investors pereptions of anageent dislosure redibility. Based on aounting and psyhology literature, I predit that investors in a positive affetive state will assess a higher level of anageent dislosure redibility due to positive interpretation and heuristi proessing of inforation, and this tendeny will be itigated by their awareness of anageent reporting inentives. The results show that, inonsistent with prior evidene, positive affet does not lead to higher assessents of anageent dislosure redibility. Instead, positive affet is assoiated with a ore systeati inforation-proessing strategy. The results suggest that the

4 psyhology literature on affet need to be refined to be applied in a anageent dislosure setting.

5 BIOGRAPHICAL SKETCH Hailan Zhou was born in a loving and aring faily in China on June 6, She reeived her Bahelor of Siene in eonois fro Fudan University in Shanghai, China in As one of the top students in her lass, she was seleted to pursue an advaned degree in eonois at Hong Kong University of Siene and Tehnology (HKUST). During her tie at HKUST, she visited the University of Mannhei in the suer of 000, where she et her then future advisor Robert Bloofield in a threeday workshop. She was intrigued by the workshop topi on experiental researh in aounting. Inspired by Rob s researh, she deided to pursue an aounting PhD in the U.S. She entered Cornell University to pursue a PhD in aounting at the Johnson Graduate Shool of Manageent in 001 and worked with Rob Bloofield sine then. After she opleted her studies at Cornell University, she joined the faulty at University of Illinois at Urbana-Chapaign in 006. iii

6 This work is dediated to y parents, for all their love and support through the ups and downs of y life. iv

7 ACKNOWLEDGMENTS I a grateful to the ebers of y oittee, Robert Bloofield (hairan), Ted O Donoghue, Martin Wells, and Steve Coate, for their valuable advie and help. In partiular, I a deeply indebted to Robert Bloofield for introduing e to experiental researh in aounting before I joined the PhD progra and for his invaluable support and enourageent throughout y years at Cornell. Without hi, I ould not have opleted this dissertation. I have also been greatly benefited fro the generous assistane fro the faulty ebers in various ways throughout y tie at Cornell. I would like to thank y olleagues in the PhD progra for going through the hardships of pursuing a PhD with e and for providing their friendship and support throughout y Cornell years. I espeially would like to thank y fellow aounting students, Bernardine Low, Nik Seybert, Bill Tayler, and Holly Yang, for their intelletual inspiration and generous help. I a grateful for the outstanding servie and support at the Johnson Shool by Nany Bell, Elizabeth Conger, Colleen Hoan, Bill Garrapy, and any unnaed here. I express thanks to y olleagues at University of Illinois at Urbana-Chapaign, espeially Clara Chen, Anne Farrell, Susan Krishe, Laura Li, Mark Peeher, and Steve Sith, for their advie and help. I appreiate valuable oents fro the workshop partiipants at Cornell University, the University of Illinois at Urbana- Chapaign, the University of Minnesota, Notre Dae, and the 006 Annual Meeting of Aerian Aounting Assoiation. Last but not least, I aknowledge the generous finanial support fro Rob Bloofield, the Johnson Graduate Shool of Manageent, and the University of Illinois at Urbana-Chapaign. v

8 TABLE OF CONTENTS Biographial Sketh iii Dediation.. iv Aknowledgents...v List of Figures..vii List of Tables...viii Chapter 1 Inentive Unertainty, Relevane, and Reliability.1 I. Introdution 1 II. III. IV. Model and hypotheses 3 The experient..18 Analysis 1 V. Conlusion 4 Appendix Referenes...60 Chapter Investor Affet and the Credibility of Manageent Dislosures..6 I. Introdution...6 II. III. IV. VI. Literature review and hypotheses The experient...74 Results...78 Conlusion and disussion..9 Appendix Referenes vi

9 LIST OF FIGURES Figure 1.1 Exaple of Best Responses....9 Figure 1. Four Senarios of Strategi Dependene...14 Figure 1.3. Expetation Errors and Welfare Effets...3 Figure 1.4. Preditive Power of Rational Expetations Equilibriu..8 Figure 1.5. Tie-Averaged Behavior. 3 Figure 1.6. Average Frequeny of Strategies and Payoff Sensitivity.36 Figure.1. Predited Effets of Manageent Copensation Shee and Investor Affet on the Credibility of Manageent Good-news Dislosures....7 Figure.. Results of Affet Manipulation...79 Figure.3. Predited Effets of Manageent Inentives and Partiipants Payent on Dislosure Credibility..85 Figure.4. Results of Path Analysis on the Effets of Manageent Copensation Shee and Partiipants Payent on Dislosure Credibility vii

10 LIST OF TABLES Table 1.1 The Experiental Design Table 1.. Influene of Rationalizability and Payoff Sensitivity on Strategy Choie..39 Table 1.3. Tie Series Properties of Strategies Table.1. Effets of Manageent Copensation Shee and Partiipants Payent on Credibility Assessents of Earnings Dislosure and Manageent...81 Table.: Effets of Manageent Copensation Shee and Partiipants Payent on the Deterinants of Dislosure Credibility Table.3. Analyses on the Deterinants of Dislosure Credibility.84 Table.4. Effets of Manageent Copensation Shee and Partiipants Payent on Inforation Proessing viii

11 CHAPTER 1 Inentive Unertainty, Relevane, and Reliability I. INTRODUCTION Aounting regulators seek to ake finanial stateent inforation both relevant and reliable, but reognize that these two goals often onflit (SFAC No., FASB 1980). Reent oves toward fair value aounting in both doesti and international reporting suggest that regulators believe the relevane of fair value easures outweighs the unreliability that arises fro the noise and bias inherent in any value estiates. Dye and Sridhar (004, hereafter DS ) provide a gae-theoreti fraework that is useful for identifying the extent to whih aounting reports should inlude inforation that (like a fair value estiate) is not only known privately by anagers, but is also anipulable by the. In this paper, I odify their odel to show that investors unertainty about anagers reporting inentives redues the extent to whih estiates should be inluded in finanial reports in equilibriu, if regulators seek to axiize investor welfare. I also use a disequilibriu analysis to show that inorporating anipulable estiates into finanial reports in the presene of high inentive unertainty is likely to ipair investors ability to assess the usefulness of the reports. I onfir these preditions in a laboratory experient. In both y odel and DS, a fir reports a weighted average of a non-anipulable signal and a anipulable signal (whih, in the absene of anipulation, would provide inreental inforation to investors). I extend DS by assuing that investors have iperfet inforation about the benefits of anipulation to the anager. This inentive unertainty iplies that investors annot perfetly undo the anager s anipulation, as they an in DS. In equilibriu, greater inentive unertainty lowers 1

12 the value-relevane of reports, and also lowers the weight on the anipulable signal that axiizes the value-relevane of the report in equilibriu (and onsequently axiizes investor welfare). Inentive unertainty indues a trade-off between relevane and reliability that is siilar to that disussed by aounting regulators: too uh weight on the anipulable inforation redues the reliability of the aggregated report, and onsequently oproises the value-relevane of the aggregated report. I also ondut a disequilibriu analysis by assuing that players use iterated deletion of doinated strategies (IDD), also alled rationalization, to narrow the set of feasible strategies, and then hoose arbitrarily fro those reaining sets. This analysis shows that greater inentive unertainty and greater weights on anipulable inforation inrease the size of the rationalizable sets, suggesting that players expetations of one another s strategies are likely to be less aurate (as in Bloofield 1995, 1997). These expetation errors result in disequilibriu outoes that har the welfare of investors by reduing their ability to value the fir aurately. The preditions of the disequilibriu analysis depend ruially on its assuptions about how players selet strategies, whih ay well be inaurate. I test these preditions by onduting an experient in whih pairs of students play the reporting gae in four settings. I anipulate two variables: investor unertainty in anagerial reporting inentives, and the weight of anagerial estiates in the aggregated report. The experiental results show that the anagers and the investors welfare losses due to inaurate expetations of their opponent s strategy inrease with weight on the anipulable inforation and with the unertainty in anageent reporting inentives. High weight on anipulable inforation also ipedes investors ability to predit anagers reporting strategies, although, high inentive unertainty does not. This ixed result arises beause players do not hoose strategies arbitrarily fro within the rationalizable sets, as assued by the disequilibriu analysis. Instead, they tend to

13 avoid high-risk strategies. When inentive unertainty is high, investors avoid risk by reduing their reliane on reports, and anagers avoid risk by responding less strongly to their inentives for anipulation. These patterns of behavior iprove expetation auray, although investors welfare is still substantially below equilibriu levels on average. Overall, the results suggest that inentive unertainty draatially redues the extent to whih regulators should inorporate fair value and other anipulable inforation into finanial reports, beause of both their equilibriu effets and their tendeny to ause disequilibriu outoes. The results also provide testable hypotheses: the atual and pereived reliability of finanial reports are likely to vary ore over tie, and be ore isaligned with eah other, when ore anipulable inforation is inorporated in finanial reports. The rest of the paper is organized as follows. Setion II presents the odel of the anager and investors and derives preditions of behavior based on the notion of strategi dependene. Setion III desribes the experient. Setion IV analyzes the experiental results. Finally, setion V provides the onlusion. II. MODEL AND HYPOTHESES In this setion I first desribe the speifiation of the odel (players, inforation, ations and inentives). I next desribe the equilibriu, in whih the anager and investor eah behave optially given the behavior of the other. I then desribe the disequilibriu analysis, whih assues that players apply a proess of rationalization to selet strategies. Finally, I present hypotheses derived fro the disequilibriu analysis. Speifiations of Model As in the DS odel, inforation about the fir s net assets oes fro a non- 3

14 anipulable signal and the anager s lai about a anipulable signal. The anager privately observes the anipulable signal of the net assets and needs to deterine the aount to report on the balane sheet. Value and Inforation. The eonoi value of the fir s net assets,ω%, follows a noral distribution with a publily known ean ω and variane σ ω. The nonanipulable signal of the fir s net assets provides a noisy easure of the eonoi value of the fir s net assets, % ω = % ω + % δ, where % δ follows a noral distribution with ean zero and variane σ δ. h The anager also akes a lai ω after observing another easure of the fir s net assets, ωf = % ω+ % εω, where ε% ω is a noral rando variable independent of the nonanipulable signal, with ean zero and varianeσ. The fir s reported net assets are deterined by a weighted average of the anager s reported anipulable signal and the non-anipulable signal of the fir s net assets aording to the equation r = λω + (1 λ) ω, where λ an be viewed as the portion of the anipulable easure in the fir s balane sheet. Investors are assued not to be able to disaggregate the anipulable and non-anipulable signals. The odel setup an be apped into the fraework in Maines and Wahlen (005). The non-anipulable signal aptures the easureent attribute of a historial ost easure and the anipulable (and therefore potentially less-reliable) signal aptures the easureent attribute of a fair value easure. The optial hoie of λ represents the optial extent to whih regulators should hoose to inorporate fair value. The optial λ also reflets the optial trade-off between relevane and reliability. Note that y odel assues that, sine aounting poliies are publi knowledge, the aggregator λ is assued to be known to investors. Despite investors knowledge about λ, I assue that investors are unable to differentiate between the nonanipulable and anipulable oponents of aounting reports. As Sunder (1997) ε h 4

15 points out, in the proess of aggregation, aountants add their knowledge and judgents about siilarities and dissiilarities of various aounts. Eah line in the aounting report is an aggregation of various inputs and aounting experts knowledge. Investors often lak the expertise to disaggregate finanial reports to ore or less reliable ites. 1 Ations and Inentives. The anager inurs an expeted ost of E ω ω [( f ) ] for stating an estiate that is higher or lower than the objetive inforation suggests, where is a fixed positive onstant. The ost to anipulate an reflet regulatory osts, reputation ost, the degree of slak in the fir s finanial position that an be used to anipulate the balane sheet, and personal effort of anipulation. I extend DS by relaxing the assuption that the anager s inentives are fixed and known by investors. Instead, in y odel, the anager s inentives to anipulate the fir s finanial reports are unertain and annot be ouniated to investors redibly. This hange allows y odel to reflet investors unertainty over whether a given report reflets optiis or pessiis (perhaps beause anagers are setting up ookie-jar reserves that provide slak to report optiistially at a later date). Speifially, I assue that the anager reeives a payoff proportional to the 1 Even at the individual aount level, investors often fae diffiulty in disaggregating an aounting ite to oponents with different degrees of anipulability. For exaple, FASB Stateent No. 13, Share-Based Payent, requires opanies to easure the ost of eployee servies reeived in exhange for an award of equity instruents based on the grant-date fair value of the award. It speifies that if an observable arket prie is not available for a share option with the sae or siilar ters and onditions, the fair value of that instruent ust be estiated. In estiating the fair value, a opany ust hoose a valuation odel, and ust develop reasonable and supportable estiates for eah assuption used in the odel. Given the oplexity, investors are unlikely to disentangle the ontributions of different inputs in deterining the estiated fair value. To fous on the interation between the anager and investors, I also assue that the investent level is deterined exogenously, rather than hosen by the anager as in DS. This siplifiation does not affet the nature of the interation between the anager s reporting deision and investors use of the fir s finanial reports. When investent is assued to be endogenous, it is deterined purely by investors reliane on the aggregated report. Thus, the results in this paper an be readily extended to an investent setting. 5

16 investors estiate of the fir s net assets, ω e, where is an inentive ultiplier that aptures the sensitivity of the anager s payoff to the investors estiate of the fir s perforane, ω e. % is assued to follow a noral distribution with ean zero 3 and variane σ. The realization of % is only observed by the anager and annot be redibly ouniated to other people. Allowing for variation in this inentive (inluding both positive and negative values) reflets the fat that firs soeties have inentives to inflate reported assets, and soeties have inentives to deflate the, and that firs ay have inentives to inflate or deflate reported assets to different extent. The agnitude of the ultiplier an be affeted by ultiple fators, suh as the proportion of stok-based opensation in the anager s inentive shee and the sensitivity of arket valuation of fir perforane to the fir s finanial reports. The investors estiate the fir s perforane based on the aggregated report of the fir s net assets. As in DS, I assue that the investors use a linear funtion of the for ϖ e( r) = a + br to arrive at their evaluation of the fir s perforane. (I prove in Appendix I.F. that a priing funtion that is linear in r is an optial response to a reporting funtion that is linear in b). Best Response Funtions and Equilibriu The anager s strategy an be haraterized as hoosing an adjustent fator, denoted θ (θ > 0), whih is ultiplied by to deterine the differene between ω and ω f. A high adjustent fator iplies that the anager s report is highly sensitive to the realization of the anager s (rando) inentive. To identify the optial hoie of θ given the investors level of reliane b, note that the anager s payoff is ( a + br) ( θ ), and (solving for the first-order ondition) the 3 The assuption that % has a ean of zero is not ruial to the qualitative aspets of the results. 6

17 bλ anager s best reporting strategy is ω( ω, εω ) = + ω + εω = θ + ω + εω. Therefore, the anager s best response funtion θ * an be written as: bλ θ * ( b) = (1) The anager s best response funtion θ * ( b) inreases linearly in his expetation of investors reliane on the report. As expeted reliane inreases, the anager benefits ore by anipulating ore of his inforation, eteris paribus. An inrease in the weight on the anipulable signal, as easured byλ, inreases the optial level of anipulation for eah expeted level of reliane. Siilarly, a derease in the reporting ost inreases the optial level of anipulation for eah expeted level of reliane. The investors strategy an be haraterized as hoosing an interept ter, a, and a slope ter, b, whih when ultiplied by the reported value r deterines a valuation of the fir s net assets. The optial interept ter is always 0, given the assuption that ω and are drawn fro a distribution with a ean of 0. Therefore, y analysis fouses on the slope ter, b, whih represents the investors reliane on the report. For any adjustent fator, θ, the investors best response an be represented as σ b*( θ ) = σ λ σ (1 λ) σ λ σ θ ω ω + ε + δ + () where a and b are as in the investors linear evaluation odel ω ( ) = a + br. The last ter in the denoinator of b * ( θ ), e r λ σ θ, indiates the effet of the expeted level of anipulation on the investors reliane. An inrease in the adjustent fator dereases the investors optial level of reliane beause the reported net assets ontain ore of anageent anipulation. The optial level of reliane is always non-negative and bounded fro above by the inforational value of the report in the absene of any anipulation. An inrease in λ or an inrease in the anager s 7

18 reporting unertainty σ dereases the optial level of reliane for every level of anipulation the investors expet. Inentive unertainty qualitatively alters investors best response funtion, relative to DS. In DS, the anager s ertain inentive allows investors to know exatly how uh the anager has altered the report, and therefore allows investors to undo the anipulation by adjusting the interept to the valuation odel. In the presene of inentive unertainty, however, investors annot know exatly how uh the anager has altered the report, or in whih diretion. As a result, investors redue the slope of the odel, effetively viewing the report as less value-relevant, with pereived valuerelevane dereasing with inreasing expetations of adjustent. Figure 1.1 depits an exaple of the anager and investors best responses. The level of adjustent fator θ is shown on the X-axis, and the level of reliane b is shown on the Y-axis. The level of reliane ranges fro 0% to 100%, and the level of adjustent fator ranges fro 0 to infinity. For ease of presentation, I report the level of adjustent fator as a perentage of 5 throughout the paper (e.g., an adjustent fator of 3 is reported as 60%), beause 5 is signifiantly higher than any reasonable level of adjustent fator in the nuerial exaples used in the paper and experient. The downward sloping line depits the investors optial reliane b*(θ) on the aggregated report for every level of adjustent fator θ. The investors optial reliane on the report inreases as the investors belief of the adjustent fator dereases. The upward sloping line depits the anager s optial agnitude of adjustent fator θ*(b) for every level of the investors reliane b on the aggregated report. The optial adjustent fator inreases as the anager s belief of the investors reliane inreases. When both the anager and investors have orret 8

19 θ *(b) Reliane (b) ( θ, b ) RE RE b*(θ) Adjustent (θ) 100 FIGURE 1.1 Exaple of Best Responses This figure shows an exaple of the anager and investor s best responses. The X- axis depits the level of the investor s reliane, and the Y-axis depits the level of the anager s adjustent fator. The downward sloping line depits the investor s optial reliane b*(θ) on the aggregated report for every level of adjustent fator θ*. The upward sloping line depits the anager s optial adjustent fator θ*(b) for every level of the investor s reliane on the aggregated report. The intersetion of the two best response funtions indiates the rational expetations equilibriu ( θ, b ). RE RE 9

20 beliefs about their opponents strategies and play the best responses to their beliefs, they are at the rational expetations equilibriu indiated by the intersetion of the two best response urves. Forally, the rational expetations equilibriu is defined as follows: Definition 1. An equilibriu relative to the aggregation rule λ onsists of a valuation equation (i) ω e (.) and a reporting funtion ω (.) suh that: The reporting rule ω (ω, ε ω ) axiizes ωe [ λω + (1 λ) ωh] ( ω ω f ) ; (ii) The valuation rule e report r. ω (.) satisfies ω [ r ] = E e [ % ω r ] for eah This definition of equilibriu requires that the anager hooses the adjustent fator that axiizes his payoff given investors valuation odel, and that the investors hoose the valuation odel that iniizes their estiation error given the anager s adjustent fator. Given this definition, the unique linear equilibriu is given in the following proposition. Proposition 1. For any aggregation rule λ [0,1], there is a unique linear equilibriu given by (i) ω [ r e ] = ( a+ br ), where σ ω b = σ + λ ( θ ) σ + λ σ + (1 λ) σ ω ε δ and a = 0; (ii) The anager s equilibriu report is given by ω ( ω, εω) = θ + ω+ εω, bλ where θ ( b) =. (See Appendix I.A. for a Proof of Proposition 1.) A hypothetial regulator seeking to axiize investor welfare in equilibriu will hoose a value of λ, denoted λ *, that axiizes the equilibriu level of b, whih 10

21 easures the value-relevane of the report (Appendix I.E. proves the optial λ that axiizes the equilibriu b also axiizes the investor welfare). Appendix I.B. shows that an inrease in inentive unertainty auses a derease in λ * in inentive unertainty dereases the reliability of the report for eah level of. An inrease anageent anipulation and effetively redues the value-relevane of the report. Thus, the regulator seeking to axiize the value-relevane of the report will redue the weight on the anipulable inforation to suppress the anager s inentive to isreport. The disussion above highlights the key differene between y odel and DS. In y odel, with inentive unertainty, the optial inorporation of estiates in the report reflets a trade-off between relevane and reliability, as opposed to DS, where λ * is unaffeted by reliability due to a fixed reporting inentive. Disequilibriu Behavior and Strategi Dependene Having haraterized equilibriu outoes, I now exaine fores that ight ake equilibriu ore or less diffiult to ahieve. The rational expetations equilibriu requires both the anager and investors to aurately predit one another s strategies. However, any gae theorists have argued that players will develop aurate expetations only if there is soe proess that leads the to do so (Binore 1987). For y analysis, I assue that players use the proess of rationalization, whih is equivalent to the proess of iterated deletion of doinated strategies" (IDD) in y setting (Bernhei 1984; Peare 1984), to eliinate all but a set of feasible strategies. In rationalization, players iteratively restrit their hoies by eliinating ations that are not the best response to at least one possible strategy not yet eliinated by the other player. To foralize this, let B denote all possible hoies of b, and let H represent all possible hoies of θ. Then define the operator R(.) to indiate the set of all best responses to a set of strategies. Let B 0 = R(H) denote the set of values of b 11

22 that are not eliinated by the first appliation of this rule, and let H 0 = R(B) denote the set of values of θ that are not eliinated by the first appliation of this rule. In suessive iterations of this thought proess, eah player eliinates strategies that are not the best response to any hoie of the other player that has not been eliinated in a previous iteration. Thus, H 1 is the set of strategies that are best responses to soe eleent of B 0, and B 1 is the set of strategies that are best responses to soe eleent of H 0. Generalizing this proess, H K is the set of strategies that are best responses to soe eleent of B K-1, and B K is the set of strategies that are best responses to soe eleent of H K-1. The index K an be viewed as the degree of rationality of the players. An infinite value of K represents oon knowledge of rationality. Following Bloofield (1995, 1997), I refer to the size of the set that reains after a given nuber of rounds as a easure of the strategi dependene of the gae. To establish forally that inreases in inentive unertainty and weight on anipulable inforation inrease strategi dependene, I alulate the produt of the slopes of the best response funtions at the equilibriu. If the best response funtions were both straight lines, rationalization would eliinate all but the equilibriu outoe if the produt of the slopes of the best response funtions was saller than 1. Even though the best response funtions are not straight lines, the produt of the slopes at equilibriu still serves as a good indiator of the degree of strategi dependene, espeially near the equilibriu. I find that an inrease in inentive unertainty and weight (when the anipulable inforation is suffiiently inforative) inreases this easure of strategi dependene, and therefore should ake equilibriu ore diffiult to ahieve. This result is suarized in the following proposition. Proposition. The produt of the slopes of the best response funtions inreases with inentive unertainty, σ. The produt of the slopes of the best response funtions inreases with weight, λ, when the anager s inforation is suffiiently 1

23 inforative. (See Appendies I.C. and I.D. for proofs). To illustrate how the power of rationalization to eliinate strategies an vary with harateristis of the reporting gae, Figure 1. shows four senarios of the best response funtions where σ ω is set to 100 and is set to 0.. The sae four senarios are used in the experient. The weight on anageent report (λ) is 40% in Senarios A and B, and 80% in Senarios C and D. The inentive ultiplier () has a standard deviation of 5 in Senarios A and C, and 15 in Senarios B and D. For the ease of ε δ illustration, σ andσ are set to 0, iplying that both the anipulable and nonanipulable signals are perfet representations of the eonoi value of the fir s net assets. This draatially siplifies the explanation of the task given to partiipants (who play the gaes depited in Figure 1.), and does not substantially alter the qualitative aspets of the analysis 4. Beause the anipulable estiate adds no inforation to the non-anipulable inforation, the lak of noise iplies that the optial weight on the anageent report is zero in all gaes; this assuption therefore eliinates a potential soure of variation aross settings, whih is not the fous of this study. Figure 1. depits how the proess of rationalization deterines the auray of expetations in four paraeterizations of the odel. In senario A, both the weight on the anager s report and the inentive unertainty are low, resulting in low strategi dependene. The investors prefer relatively high reliane even if their expetation of the anager s adjustent level is high, while the anager prefers a relatively low adjustent level even if his expetation of the investors reliane is high. As a result, ε δ 4 Setting σ andσ to zero does not hange the anager s best response funtion. It does redue the slope of the investors best response, and therefore slightly redues strategi dependene. However, the qualitative preditions of the odel are not hanged. In partiular, all the proofs provided in the Appendies are based on the general odel with non-zero σ ε and σ δ. 13

24 FIGURE 1. Four Senarios of Strategi Dependene This figure shows four senarios of strategi dependene that are used in the experient. For eah senario, the X-axis depits the level of the investor s reliane, b, and the Y-axis depits the level of the anager s adjustent fator, θ. The downward sloping line depits the investor s optial reliane b*(θ) on the aggregated report for every level of the anager s adjustent fator θ*. The upward sloping line depits the anager s optial level of adjustent fator θ*(b) for every level of the investor s reliane on the aggregated report. The intersetion of the two best response funtions indiates the rational expetations equilibriu ( θ RE, bre ).The value of the fir s net asset is norally distributed with ean zero and standard deviation 10. Both σ ε andσ δ are zero. The inentive ultiplier,, has a standard deviation of 5 in senario A and senario C and 15 in senario B and senario D. The weight on the anager s adjustent is 40% in senario A and senario B and 80% in senario C and senario D. The shaded areas show zero- and first-order rationalization for both the anager and investor. The areas shaded with and indiate the anager s strategies that are eliinated in the zero- and first-order rationalization. The areas shaded with and ontain the investor s strategies that are eliinated in the zero- and first-order rationalization. Infinite iterations of the rationalization proess redue the rationalizable sets to zero in senarios A, B and C with a uh slower speed for senario C. Infinite iterations of the rationalization proess leaves the rationalizable set to a range for senario D. Strategi dependene is the lowest in senario A and the highest in senario D. B i denotes the set of reliane that reains after ith-order rationalization. H i denotes the set of adjustent fator that reains after ith-order rationalization. Produt of the best response urves at equilibriu is a easure of the degree of strategi dependene. Strategi dependene is high when the produt is greater than 1. 14

25 Senario A: Low Weight, Low Inentive Unertainty Senario B: Low Weight, High Inentive Unertainty Reliane (b) θ *( b) ( θ, b ) RE RE b*( θ ) Reliane (b) θ *( b) ( θ, b ) RE RE b*( θ ) Adjustent (θ) (B 1 = [40, 100], H 1 = [4, 40]) (B = 89, H = 36) Produt of the slopes at equilibriu = Senario C: High Weight, Low Inentive Unertainty Adjustent (θ) (B 1 = [85, 100], H 1 = [0, 40]) (B = 63, H = 6) Produt of the slopes at equilibriu = 0.4 Senario D: High Weight, High Inentive Unertainty Reliane (b) θ *( b) ( θ, b ) RE RE b*( θ ) Reliane (b) ( θ, b ) RE RE θ *( b) b*( θ ) Adjustent (θ) (B 1 = [8, 100], H 1 = [16, 80]) (B = 56, H = 44) Produt of the slopes at equilibriu = Adjustent (θ) (B 1 = [3, 100], H 1 = [, 80]) (B = [4, 98], H = [4, 76]) Produt of the slopes at equilibriu= 1.378

26 B 0 = [50, 100] and H 0 = [0, 40]. The flatness of the best response urves iplies that the next iteration of rationalization eliinates even ore strategies, with B 1 = [85, 100] and H 1 = [0, 40]. One ore iteration of the rationalization proess eliinates soe doinated strategies and liits the final rationalizable set of strategies to the RE equilibriu. Coparing aross senarios, Figure shows that two iterations of rationalization leave larger sets of strategies reaining when the report plaes ore weight on the anipulable inforation (oparing A to C and B to D), and when inentive unertainty is greater (oparing A to B and C to D). Additional iterations tell a slightly different story: with infinite iterations, the rationalization proess eliinates all strategies other than the equilibriu outoe in Senarios A, B and C, although the proess is far slower in senario C; however, additional iterations eliinate hardly any additional strategies in Senario D, in whih both the weight on the anager s report and the reporting inentive unertainty are high. In Senario D, strategi dependene predits that the RE equilibriu is likely to lose preditive power on subjets behaviors. Hypotheses The preeding analyses suggest that it is harder for the anager and investors to for orret expetations of their opponent s strategy when either higher weight on anipulable estiates or higher inentive unertainty reates high strategi dependene. I therefore predit that these aspets of the reporting environent lead players expetations to be less aurate, and lead players to deviate ore fro equilibriu. H1: Managers assessents of investors reliane and investors assessents of anagers adjustents are less aurate when reports plae ore weight on anagers value estiates, and when anagers inentives are ore unertain. 16

27 H: Managers anipulations and investors reliane deviate ore fro equilibriu when reports plae ore weight on anagers value estiates, and when anagers inentives are ore unertain. H fouses on absolute, rather than signed deviations, beause there is no reason that tie-averaged strategies ust deviate fro equilibriu over any rounds, just beause no single round is lose to equilibriu 5. Note also that the analyses on the easureents of strategi dependene see to suggest that the effet of eah variable is stronger when the other variable is at a high level. In partiular, the rationalizable set of strategies is nonzero, and the produt of the two best response urves is greater than 1, only when both weight and inentive unertainty are high. This result suggests that the weight plaed on the anager s estiate and the unertainty in the anager s reporting inentives ay interat. However, beause strategi dependene is used only as a heuristi to generate qualitative preditions about unknown equilibrating proesses, I do not hypothesize an interation. It is possible that inaurate expetations and deviations fro equilibriu arise not fro players inability to settle into a stable pattern of behavior, but fro their tendeny to settle into a stable pattern in whih expetations are inorret and far fro equilibriu. To rule out this possibility, I exaine instability in behavior over tie. H3: Managers anipulations and investors reliane vary ore over tie and onverge to equilibriu ore slowly when reports plae ore weight on anagers estiates, and when anagers inentives are ore unertain. Note that the hypotheses above are not suseptible to the ritiis (artiulated by Kaheleier (1996)) that they are foregone onlusions as long as the experient suessfully indues the orret payoffs and utility funtions assued by the 5 Hofbauer and Sigund (1988) show that tie average of players strategies onverge to equilibriu under ertain onditions. 17

28 equilibriu odel. Instead, the hypotheses are founded on an essentially psyhologial odel of the proess (rationalization) by whih players hoose their strategies. The hypotheses would be rejeted if players were soehow able to selet equilibriu strategies even when any other strategies are rationalizable. The hypotheses would also be rejeted if harateristis of the players payoff funtions ight alter how they hoose aong strategies that survive rationalization. In partiular, the analysis ignores the fat that high inentive unertainty draatially inreases the possible losses that the anager ould fae by hoosing a high adjustent fator, or that investors ould fae by hoosing high reliane, even though these strategies survive rationalization. To the extent that players hoies are deterined by the risks involved in hoosing strategies, rather than siply whether the strategies are ever best responses, the preditions of strategi dependene ay not be upheld. Beause there is no theory that predits how players risk preferenes ight interat with the predition of strategi dependene in deterining their hoies, I do not for hypotheses on the effet of risk preferenes. III. THE EXPERIMENT Design To test the hypotheses laid out above, I onduted a laboratory experient in a (high vs. low weight) x (high vs. low inentive unertainty) x 10 (repetition) x (order) ixed design as shown in Table 1.1. All variables exept order were anipulated within-subjets. The design also inludes two additional 10-round bloks for the high weight, high inentive unertainty senario to provide the subjets the best hane of learning in the high strategi dependene senario. The paraeter values in the experient are idential to those used in generating Figure 1.. Order of treatents was anipulated between-subjets to ontrol for a potential order effet. A within- 18

29 subjets design ontrols for variane due to differenes aross subjets and enhanes the power of the experient. A within-subjets design an also ause deand effets, but these deand effets are unlikely to hange the auray of subjets expetations about other subjets hoies (whih is the fous of the experient). TABLE 1.1 The Experiental Design Treatent Blok I Blok II Blok III Blok IV Blok V Blok VI Order I LoW, LoU HiW, HiU LoW, HiU HiW, HiU HiW, HiU HiW, LoU Order II HiW, LoU HiW, HiU HiW, HiU LoW, HiU HiW, HiU LoW, LoU *Note: LoW, LoU = low weight and low inentive unertainty (Senario A); LoW, HiU= low weight and high inentive unertainty (senario B); HiW, LoU= High weight and low inentive unertainty (senario C); and HiW, HiU= High weight and high inentive unertainty (senario D). 40 students at a private university partiipated in the experient. Half of the subjets were randoly assigned the role of anager throughout the session, and the other half were assigned the role of investor. Subjets identities were held anonyous throughout the session. To avoid the possibility that subjets behaviors would be affeted by real-world knowledge assoiated with the roles of anager and investor, all the instrutions and experiental aterials were worded neutrally. The anagers were alled reporters, and the investors were alled appraisers. For the ease of presentation, I refer to the players as anagers and investors in the paper. (See Appendix II for instrutions to partiipants.) Eah anager was randoly paired with an investor at the beginning of the experient and played with the sae investor for the entire session. Fixed pairing is preferable to rando pairing beause it requires fewer subjets for the sae statistial power, inreases the opportunity for subjets to learn their opponents strategy, and better reflets the interation between anagers and investors in the real world. A 19

30 potential ost of this hoie is that fixed pairs ay allow players to use ulti-period strategies, and equilibria of the repeated gae ay differ fro the equilibriu of the stage gae if players an identify a yle of outoes that provide higher average payoffs for eah player than their equilibriu payoffs in the stage gae (Auann, 1976). However, I test for and find no evidene of suh behavior in the analysis. The Task In eah round of play, eah anager entered an expetation of the investor s hoie of reliane, and also hose a level of adjustent. Their oputer sreens (see Appendix III for sreen shots) showed the payoff they would expet to reeive fro their strategy given that their expetation was orret. Managers were allowed to alter their expetations and strategy hoies as often as they wished before onfiring their hoies. Siilarly, eah investor entered an expetation of the anager s hoie of adjustent fator, and also hose a level of reliane. The possible hoie for the level of reliane ranged fro 0% to 100%, and for the level of adjustent fro 0 to 5 (where 5 is signifiantly higher than any reasonable level of adjustent predited by the odel). Atual payoffs in eah round were deterined by the average payoff reeived fro 100 representative realizations of the various rando variables in the odel (the error in anager s private inforation and anager s inentive). The use of 100 reports instead of one report per round has several benefits. It provides better easures of subjets atual strategies, rather than strategies assoiated with individual realizations of base value and inentive ultiplier of a report. The payoffs alulated based on the average result of all 100 reports are ore oparable aross rounds, providing eah player with ore preise feedbak about the other player s strategy, therefore enhaning learning (Bloofield,1994). In addition, I provided the subjets with graphs of the best response urves of their 0

31 own role in eah senario. Providing the best response urves redues the noise in subjets strategies and is likely to inrease the possibility for the subjets to reah the equilibriu. In eah round, both players ade their deisions siultaneously. After both players had ade their hoies, they oved on to the feedbak sreen where they reviewed their opponent s atual strategy and their atual payoff alulated based on the atual strategies played. In addition, both the deision-aking and feedbak sreens showed their deision history up to the last 5 rounds to failitate their expetation foration. Adinistration Eah session began with a short training session during whih subjets learned about the experient and beae failiar with the task sreen in four pratie rounds. At the end of the session, subjets answered debriefing questions regarding their understanding of the experient and their deision-aking proess. Subjets were told at the beginning of the experient that their total laboratory winnings sued over all rounds exluding pratie rounds would be used to deterine their ash winnings in US dollars. They were also told that eah subjet s perforane would be opared to the average perforane of the subjets in the sae role in deterining their ash winnings. This approah redues the hane that a player believes that one s payoff depends on the role that he/she plays. On average, eah subjet reeived $0 for the 80 inute session in addition to a iniu show-up fee of $5. IV. ANALYSIS This experiental design generates one blok of 10 rounds for eah of the four senarios, along with an additional two bloks of 10 rounds eah for the high strategi dependene senario (High-Weight, High-Inentive Unertainty). For hypothesis tests, I only use the first bloks of all senarios in order to have a balaned statistial design. 1

32 In y exploratory analysis of dynai behavior, I inlude all three bloks of the high strategi dependene senario and exaine its tie series properties in detail. A total of 0 independent pairs played the four senarios. To ontrol for the dependene in subjets responses aross rounds within eah pair, dependent variables in the ANOVA analyses are generated by averaging relevant dependent variables over rounds within eah treatent per pair. This provides in total 0 x 4 = 80 data points with 4 generated by eah pair. All tests of hypotheses use a repeated-easures analysis to aount for the fat that eah ohort provides four (non-independent) observations. Hypothesis Tests H1 predits that greater weight on the anager s estiate and greater inentive unertainty redues the auray of partiipants expetations. I use two types of easureents to test this hypothesis: the absolute errors in subjets expetations and the osts to the due to their expetation errors. I first alulate the seond easure as the absolute differene between eah subjet s atual payoff and the best payoff they ould have obtained had they been able to predit their opponent s strategy perfetly. This easure aptures the true loss funtion of the players (rather than using the linear loss funtion assued by the first easure), and also reveals the welfare onsequenes of expetation errors. I then alulate the absolute differene between the subjet s opponent s hoie and the subjet s expetation of that hoie iplied by their own hoie (the hoie to whih their own is a best response). Figure 1.3 displays the results based on round 3 to round 10. Subjets responses in round 1 and round are deleted to avoid noise due to inexperiene with the gae. Inluding the first two rounds in eah senario does not hange the onlusion. Panel A of Figure 3 shows the harts of the average payoff losses due to expetation errors and the average absolute errors in subjets' expetations of their opponents' strategies

33 FIGURE 1.3 Expetation Errors and Welfare Effets Panel A presents the average payoff losses due to the errors in expetations and the average absolute errors in subjets' expetations of their opponents' strategies over round 3 to round 10 for eah senario. Panel B presents the ain effets of weight and inentive unertainty and their interation on the payoff losses and expetation errors. PayLossInv (PayLossMA) is defined as the differene between investors/anagers' atual payoffs and the optial payoffs they would have obtained if their expetations were perfetly aurate. By onstrution, PayLossInv (PayLossMA) is always nonpositive. ExpRel(ExpAdj) is defined as anagers (investors)' expetation of their opponent's reliane (adjustent), alulated fro the optial response to their own strategies. The signifiane levels for the ain and interation effets are oputed using repeated-easures ANOVA analysis. All assoiated p-values are two-tailed. 3

34 4 Panel A: Average payoff losses due to expetation errors and average absolute expetation errors.

35 FIGURE 1.3 (Continued) 5 Panel B: Statistis of the ain and interation effets Variable Effet F-statistis p-value PayLossInv Weight Inentive Unertainty Weight x IU PayLossMA Weight Inentive Unertainty Weight x IU ExpAdj-Adjustent Weight Inentive Unertainty Weight x IU ExpRel-Reliane Weight Inentive Unertainty Weight x IU

36 aross the onditions of inentive unertainty and weight. Panel B of Figure 1.3 presents the ain and interation effets of weight and inentive unertainty on payoff losses and expetation errors. Consistent with H1, the welfare onsequenes of expetation errors are all statistially signifiant and in the predited diretion. For the investors, inreasing in weight redues investors average payoff relative to their best payoffs possible by 8.01 (p-value < 0.01) and inreasing in inentive unertainty dereases the investors average payoff relative to their best payoffs possible by (p-value = 0.0) 6. For the anagers, inreasing in weight redues the anagers average payoff by (pvalue = 0.03) and inreasing in inentive unertainty dereases their average payoff by (p-value = 0.04). The interation between weight and inentive unertainty is highly signifiant for both the anagers and investors (p-values = 0.03 for both the anagers and investors). The siple eans of subjets payoff losses further reveal that the interation effet is driven by the uh higher payoff losses in the high strategi dependene senario. In ontrast, payoff losses are relatively sall when either weight or inentive unertainty is low. These results strongly support H1. Measuring absolute errors in expetations (rather than the payoff effet of those errors) reveals a slightly different story. Neither the effet of weight nor the effet of inentive unertainty signifiantly influenes anagers absolute expetation errors (p-value = 0.47 and p-value = 0.90 respetively). Weight signifiantly redues investors absolute expetation errors (p-value = 0.03), but inentive unertainty atually dereases investors expetation errors (p-value = 0.0). As disussed in Setion II, the weak effet of inentive unertainty on expetation errors ay arise beause players do not hoose arbitrarily fro within the set of 6 All p-values presented in the paper are two-sided, unless otherwise indiated. 6

37 feasible strategies reaining after iterated deletion of doinated strategies. I test this explanation after presenting evidene for hypotheses H and H3. H states that strategi dependene redues the preditive power of the rational expetations equilibriu. Siilar to the analysis for H1, I opute two types of easures to test this hypothesis: the absolute deviations of their payoffs fro the equilibriu payoffs and the absolute deviations of subjets strategies fro the equilibriu values. Both easures are averaged over the last 8 rounds in eah senario. The results are reported in Figure 1.4. Consistent with H, subjets payoffs deviate ore fro the equilibriu payoffs when strategi dependene is higher. An inrease in weight signifiantly inreases the deviation of the investors payoff (anagers payoff) fro the equilibriu payoff with a p-value of 0.01 (p-value < 0.01), and an inrease in inentive unertainty signifiantly inreases the deviation of the investors payoff (anagers payoff) with a p-value of 0.01 (p-value < 0.01). The interation between weight and inentive unertainty is signifiant for the anagers (p-value = 0.01) and arginally signifiant for the investors (p-value = 0.07, onesided). Overall, the evidene is onsistent with H, whih predits that strategi dependene redues the preditive power of the REE. Figure 1.4 also shows the results on the absolute deviations of subjets strategies fro equilibriu behavior. An inrease in weight inreases both the absolute deviations of the investors reliane and the anagers adjustent fro equilibriu (p-value < 0.01 and p-value = 0.01 respetively). However, siilar to the findings on the absolute expetation errors in Figure 3, the effet of inentive unertainty is insignifiant for either the absolute deviation of the investors reliane (p-value = 0.15) or the absolute deviations of the anagers adjustent (p-value = 0.37). H3 predits that subjets strategies flutuate ore when strategi dependene is 7

38 FIGURE 1.4 Preditive Power of Rational Expetations Equilibriu Panel A displays the average deviations of subjets' payoffs fro the equilibriu payoffs and the average absolute deviations of Reliane and Adjustent fro the rational expetations equilibriu over the last eight rounds in eah of the four senarios. Panel B displays the ain and interation effets of weight and inentive unertainty for eah of the four variables. The variable Payoff* represent the equilibriu payoff. The variables Reliane* and Adjustent* denote the equilibriu reliane and adjustent. Signifiane levels for all interations and ain effets are oputed using repeated-easures ANOVA analysis. All assoiated p-values are twotailed. 8

39 9 Panel A: Average absolute deviations of payoffs and strategies fro equilibriu

40 FIGURE 1.4 (Continued) Panel B: Statistis for the ain and interation effets 30 Variable Effet F-statistis p-value Payoff - Payoff* (Investor) Weight Inentive Unertainty Weight x IU Payoff - Payoff* (Manager) Weight Inentive Unertainty Weight x IU Reliane - Reliane* Weight <.0001 Inentive Unertainty Weight x IU Adjustent - Adjustent* Weight Inentive Unertainty Weight x IU

41 higher. Support for H3 rules out the possibility that inaurate expetations and deviations fro equilibriu arise beause players settle on a onsistent disequilibriu outoe. The effets of strategi dependene on the standard deviations of reliane and adjustent are shown in Figure 1.5. Panel A presents the harts of the ell eans of the standard deviations. Panel B suarizes the ain and interation effets of weight and inentive unertainty. The effets of weight on the standard deviations of both reliane and adjustent support H3. An inrease in weight signifiantly inreases the standard deviation of investors reliane and the standard deviation of anagers adjustent. However, the effet of inentive unertainty is only signifiant on the variation of investors reliane in the predited diretion, but is signifiant in the opposite diretion to the hypothesis on the variation of anagers adjustent. To hek whether high variations are indeed driven by strategies varying round by round, I alulate the absolute hanges in investors reliane and anagers adjustent in onseutive rounds over round 3 to round 10. Results are displayed in panel B of Figure 1.5. The behaviors of the absolute hanges in reliane and adjustent onfir that the higher standard deviations in subjets strategies are ostly driven by flutuation in their strategies. High weight is assoiated with greater absolute hanges in both reliane and adjustent. And high inentive unertainty indues greater absolute hange in reliane. Consistent with the explanation of payoff sensitivity, high inentive unertainty is assoiated with lower absolute hange in adjustent. 7 7 To ensure that absolute deviations fro equilibriu are not due to subjets onsistently playing strategies lower or higher than the equilibriu, I also analyze tie-averaged strategy hoies. If the deviations are driven by differenes in subjets ability to develop aurate expetations, tie-averaged behaviors should be loser to the equilibriu preditions. Speifially, I opare subjets tieaveraged payoffs and tie-averaged strategies over the last 8 rounds in eah senario to the equilibriu strategies and payoffs. Exept for the reliane in the high inentive unertainty senarios, the average strategies over the last 8 rounds are statistially indistinguishable fro the equilibriu strategies. Even in the high inentive unertainty senarios, the average deviation fro equilibriu aounts for only a sall portion of investors payoff losses relative to equilibriu. 31

42 FIGURE 1.5 Tie-Averaged Behavior Panel A displays the average deviations of subjets' payoffs fro the equilibriu payoffs and the average deviations of Reliane and Adjustent fro the rational expetations equilibriu over the last eight rounds in eah of the four senarios. Panel B displays the ain and interation effets of weight and inentive unertainty for eah of the four variables. The variable Payoff* represent the equilibriu payoff. The variables Reliane* and Adjustent* denote the equilibriu reliane and adjustent. Signifiane levels for all interations and ain effets are oputed using repeatedeasures ANOVA analysis. All assoiated p-values are two-tailed. 3

43 33 Panel A: Average deviations of payoffs and strategies fro equilibriu

44 FIGURE 1.5 (Continued) Panel B: Statistis of the ain and interation effets of weight and inentive unertainty 34 Variable Effet F- statistis p-value Payoff - Payoff* (Investor) Weight Inentive Unertainty Weight x IU Payoff - Payoff* (Manager) Weight Inentive Unertainty Weight x IU Reliane - Reliane* Weight Inentive Unertainty Weight x IU Adjustent -Adjustent* Weight Inentive Unertainty Weight x IU

45 Overall, the evidene supports H3 that subjets adapt to past strategies and hange their strategies over tie, and ore so when strategi dependene is higher and payoff sensitivity is lower. High variations in strategies ake it harder for subjets to onverge to equilibriu due to noisier perforane feedbak. The following setion investigates these anoalous results in ore details. Analysis of Anoalous Results My hypotheses assued that players hose strategies arbitrarily aong those that survive at least two iterations of rationalization. In this analysis, I exaine whether the weak effet of inentive unertainty on expetation errors arises beause players avoid strategies with high payoff risk, even though they ay be onsistent with several iterations of rationalization. To test this onjeture, I alulate the average sensitivity of the players payoffs to their opponents strategies for eah level of their own strategy, and also alulate the range of strategies onsistent with seond-order rationalization (B and H ). 8 The average sensitivity of both players payoffs for all four senarios is depited as solid lines in Figure 1.6, superiposed over a histogra indiating the average frequenies of players strategies for eah level, shown as light grey bars. The graphs show that strategies inonsistent with seond-order rationalization are rarely seleted. Within the reaining strategies, those with very high payoff sensitivity are also rarely seleted, partiularly in the senarios with high payoff unertainty. To forally establish this tendeny, I ondut a regression analysis on the frequeny of strategies. The independent variables inlude a binary variable with a value of 1 if the strategy satisfies seond-order rationalization and a value of 0 otherwise (The analysis based on zero-order or first-order rationalization gives siilar 8 The players payoffs are onotoni in their opponent s strategy for eah level of their own strategy. Speifially, investors payoff dereases onotonially in the anager s anipulation and the anager s payoff inreases onotonially in investors reliane, eteris paribus. 35

46 FIGURE 1.6 Average Frequeny of Strategies and Payoff Sensitivity This figure shows the average frequeny of players strategies and players average payoff sensitivity to their opponents strategies. Panel A to Panel D show for all 4 senarios the average frequeny of investors reliane, depited as grey vertial bars, and the investors average payoff sensitivity to the anager s anipulation, depited as blak dotted lines. Panel E to Panel H show the average frequeny of the anager s anipulation and average payoff sensitivity to investors reliane. The frequeny of strategies is displayed on the left vertial axis and the payoff sensitivity is displayed on the right vertial axis. The two dashed lines indiate the range of strategies that survive the seond-order rationalization. 36

47 Panel A: Low Weight, Low Inentive Unertainty Panel B: Low Weight, High Inentive Unertainty 37 Reliane Reliane Panel C: High Weight, Low Inentive Unertainty Panel D: High Weight, High Inentive Unertainty Reliane Reliane

48 FIGURE 1.6 (ontinued) Panel E: Low Weight, Low Inentive Unertainty Panel F: Low Weight, High Inentive Unertainty Adjustent Adjustent 38 Panel G: Low Weight, Low Inentive Unertainty Panel H: Low Weight, High Inentive Unertainty Adjustent Adjustent

49 results), payoff sensitivity, and an interation between payoff sensitivity and the binary variable. Results shown in Table 1. provide evidene onsistent with the hypothesis. Players are ore likely to hoose strategies that satisfy seond-order rationalization (both p-values < 0.01), and aong those strategies, are less likely to hoose strategies that result in highly variable payoffs (p-value < 0.01 and p-value = 0.05 for the frequenies of reliane and adjustent respetively). TABLE 1. Influene of Rationalizability and Payoff Sensitivity on Strategy Choie This table presents the regression analysis of the frequeny of strategies. The independent variables inlude a binary variable (Duy) with a value of 1 if the strategy satisfies seond-order rationalization and a value of 0 otherwise, payoff sensitivity (Pay Sensitivity), and an interation between the binary variable and payoff sensitivity. Payoff sensitivity is alulated as the average sensitivity of players' payoffs to their opponents' strategies for eah level of their own strategy. The regression odel: Frequeny = α + β1*duy + β*pay Sensitivity + β3*(pay Sensitivity*Duy) Dependent Variable α β 1 β β 3 Adjusted R Frequeny of Reliane P-value < Frequeny of Adjustent P-value < The result indiates that an inrease in inentive unertainty also inreases players payoff sensitivity to their opponents strategies, whih otivates players to respond strongly to their inentives and to avoid risky strategies. Therefore, inreasing anageent inentive unertainty dapens the effet of strategi dependene by inreasing players payoff sensitivity. Suppleentary Analysis 39

50 While the theory of rationalization assues that players base their strategy hoies on an analysis of best response funtions, the preditions of rationalization are very siilar to the long-run preditions that would be derived fro analysis of adaptive proesses that assue that players alter their strategies in response to prior experiene in the gae (see Moulin 1984; Sauelson and Zhang 199). Adaptive proesses also predit learning behavior in the short run. I now ondut exploratory analyses of short-ter learning behavior, whih ay shed light on how the atual reliability of finanial reports (as deterined by anagers adjustent fators) and their pereived reliability (as deterined by investors reliane) ay vary over tie. To exaine the speed of onvergene, I estiate the following regression odel for both expetation errors and absolute deviations fro equilibriu: DV = α + SDduy + β ( ) 1Round + β Round SDduy, where DV denotes appropriate dependent variable, Round is the nuber of rounds elapsed in the senario, and SDduy is an indiator that takes a value of 1 for the low strategi dependene senario (Low-Weight, Low-Inentive Unertainty) and 0 for the high strategi dependene senario (High-Weight, High-Inentive Unertainty). A signifiant negative oeffiient on the third ter in the regression odel, β, would suggest a faster onvergene in the low strategi dependene senario. As Table 1.3 shows, the results on the absolute deviations fro equilibriu and investors expetation errors are all onsistent with this hypothesis. 9 The oeffiient β is negative and statistially signifiant in all four odels. The evidene strongly supports the strategi dependene arguent that subjets learn faster and onverge to equilibriu at a higher speed when strategi dependene is lower. 9 The results are siilar when only the first blok of senario D is inluded in the regressions. 40

51 TABLE 1.3 Tie Series Properties of Strategies This table presents the results of the regression odels that opare the speed of onvergene of the four variables between the low and high strategi dependene senarios (senarios A and D). Round is the nuber of rounds elapsed in the senario. SDduy is an indiator that takes a value of 1 for the low strategi dependene senario. All three bloks of the high strategi dependene senario are inluded in the regression analysis. The regression odel: DV = α+sdduy+β 1 *Round+β *(Round*SDduy) Dependent Variable α SDduy β1 p-value β p-value Adjusted R ExpRel-Reliane < ExpAdj-Adjustent < Reliane - Reliane* Adjustent - Adjustent* < To exaine how atual and pereived reliability hange over tie, I estiate the following regression odels for investors and anagers in eah of the four senarios: For investors: Reliane Reliane = α + β ( ExpAdj Adj ) + β ( ExpRel Reliane ) t t 1 1 t 1 t 1 t 1 t 1 + β ( Reliane Reliane ) + β ( Adj Adj ) 3 t 1 t 4 t 1 t For anagers: Adj Adj = α + β ( ExpRel Reliane ) + β ( ExpAdj Adj ) t t 1 1 t 1 t 1 t 1 t 1 + β ( Adj Adj ) + β ( Reliane Reliane ) 3 t 1 t 4 t 1 t where Adj, Reliane, ExpAdj and ExpRel are defined as in Figure 3. The regression results are presented in Table 4. The adjusted R s range fro 0.39 to 0.57 explaining about half of subjets hanges in strategies. For Investors (anagers), β 1 is positive (negative) and statistially signifiant for all senarios. A positive (negative) β 1 for investors (anagers) suggests that when anagers adjustent (investors reliane) in 41

52 the previous round was lower than expeted investors (anagers) are likely to inrease (redue) their reliane (adjustent) in urrent round. This is onsistent with players oving toward their best responses in the previous round. β in the investor regression odel is positive and statistially signifiant in all four senarios, suggesting that when anagers adjustent in the previous round was higher than optial investors inrease their reliane in urrent round. Siilarly, β in the anager regression odel is signifiantly positive in senarios C and D, suggesting that when investors reliane in the previous round was lower than optial, anagers inrease their adjustent in urrent round. The evidene shows that subjets antiipate their opponents ations and at aordingly. Both β 3 and β 4 are either insignifiant or signifiantly negative. This suggests subjets tend to reverse the hanges in their strategies in the previous round and reat to hanges in their opponents strategies. These analyses suggest that pereived and atual reliability are likely to hange in preditable ways over tie, partiularly when strategi dependene is high. It would therefore be an oversiplifiation to assue aounting anipulation and investors reliane are at the equilibriu levels, espeially when anagers have great disretion on finanial reports and fae greater unertainty in reporting inentives. V.CONCLUSION This paper odifies Dye and Sridhar s [004] fraework for exaining the optial trade-off between relevane and reliability when the anager an provide relevant but potentially anipulable (and therefore unreliable) inforation to aounting reports. An equilibriu analysis shows that the optial inorporation of the anager s lais dereases as investors beoe ore unertain about the anager s reporting inentives. A disequilibriu analysis further shows that equilibria are less likely to be attained to the detrient of investors when the 4

53 aounting report plaes greater weight on the anager s lais and when investors are less ertain about the anager s inentives. A laboratory experient largely onfirs this predition, and shows that suh harateristis of the reporting environent signifiantly redue investor welfare. The results have ipliations for regulators, given the urrent oveent toward extending the use of fair value easureents in finanial reports. Fair value easureents are often onsidered to be ore relevant but less reliable due to easureent errors and anipulation. My results show that failing to onsider the unertainty in anageent reporting inentives ay result in overstating the degree to whih fair value or other anipulable estiates should be inorporated into aounting reports. Moreover, inorporating ore fair value easureents ay have an unintended onsequene in aking the atual reliability of finanial reports ore variable and less preditable for investors by inreasing the strategi dependene between the anager and investors. The welfare analysis indiates that investors interest is likely to be hared when anageent reporting inentives are unertain. Suppleentary analyses suggest that the arket-pereived reliability of finanial reports does not always equal the atual reliability, and that both ay vary over tie. Therefore, value-relevane studies that assue an effiient arket are likely to isestiate the atual relevane and reliability of the aounting inforation under exaination. Aboody, Hughes, and Liu (00) reognize this issue and propose to inorporate inforation in delayed future arket reations in estiating valuerelevane oeffiient. To the extent that anageent investent deisions are based on expeted arket reations, unpreditable arket use of finanial reports is likely to ause ineffiient investent deisions. This onern is shared by Liang and Wen (005) and Plantin, Sapra, and Shin (005). Liang and Wen show analytially that an inrease in 43

54 aounting noise and anipulation indues greater arket ispriing, and onsequently, auses a less effiient investent deision. Plantin et al. argue that shifting toward fair value aounting ay ause exessive artifiial volatility that degrades the inforational value of arket pries and indues less effiient investent deisions. Certain harateristis of the experient ay liit the generalizability of the results to real arkets. In the experient, I use a two-player gae to test the effet of strategi dependene on the preditive power of equilibriu. Analyses on tieaveraged strategies (untabulated) show that the rational expetations equilibriu has fairly good preditive power on players tie-averaged behaviors. If investors beliefs are unorrelated, the law of large nubers ay allow investor reliane to reah a steady state. In addition, other arket and institutional fators not aptured in the urrent experiental setting, suh as the existene of arbitrageurs and auditing servies, are also likely to have an ipat on the anager-investors interation. Alternatively, the addition of ore players (and therefore ore strategi unertainty) ay ake equilibriu even ore diffiult to ahieve. 44

55 I: Proofs APPENDI X A. Proof of Theore 1 Proof: Given the valuation odel, ω e( r ) = a + br and realizations (, ω, ε ω ) of ( %, % ω, % εω ), the anager hooses ω to axiize ( a + br) ( ω ω f ) bλ The first order ondition with respet to ω iplies: ω ( ω, εω ) = + ω + ε Sine ωh = ω + δ, we an write the aggregated report r as: r = λω ( ω, ε ) + (1 λ) ω ω bλ = ω + λ( + εω ) + (1 λ) δ Therefore, applying a ethod of standard linear regression, we have: h ω σ E[ % ω r] = ω + ( r ω λe[ v]) σ λ λ σ λ σ ω ω + var( v) + ε + (1 ) δ where v is the aount of anipulation in the anager s report. In the equilibriu, bλ bλ v has the following properties: E[ v] = E[ ] = and bλ var( v) = ( ) σ Fro this, it is lear that the expression for b in the valuation odel is σ ω b = bλ σ + λ ( ) σ + λ σ + (1 λ) σ ω ε δ (A1) bλ The onstant a has the following for in equilibriu: a = (1 b) ω bλ When ω and are zero, it is lear that equilibriu a is zero. 45

56 B. Derivation of the optial λ that axiizes b Define the optial λ, denoted λ *, as the aggregator that axiizes the inforation value of the aggregated report, i.e. b. We an rewrite equation A1 as: bλ bσ ω + bλ ( ) σ + bλ σ ε + b(1 λ) σ δ σ ω = 0 (B1) Solving for λ * using ipliit differentiation, we get: b b λ b b λ b b σ + 3 σ 4 (1 ) (1 ) 0 + σ + λ σ + bλσ + λ σ b λ σ = ω λ λ ε λ ε δ λ δ b b λ b λ ( σ ω + 3 σ + λ σ ε + (1 λ) σ δ ) bσ δ + 4 σ ( ) 0 + bλ σ ε + σ δ = λ 3 3 b λ bσ 4 ( ) b b δ σ λ σ ε + σ δ = 4 λ b λ σω + 3 σ (1 ) + λ σ ε + λ σδ Sine the denoinator is always greater than zero, setting b to zero iplies the λ nuerator ust be zero: 3 b λ σ δ σ ( ) 0 λ σ ε + σ δ = (B) We also know that λ * and the axiu b satisfy equation B1. Therefore, λ * and the axiu b an be deterined by equations B1 and B. Due to the oplexity of the ters involved, λ * and the axiu b annot be solved expliitly. However, we an define λ ' as the optial λ when σ is zero, whih orresponds to the ase in Dye and Sridhar [004]. When σ is zero, the optial λ an be deterined fro the following equation: σ λ( σ + σ ) = 0 (B3) δ ε δ 46

57 Given σ δ and σ ε, equations B and B3 iply that: 3 b λ * λ '( σ ε + σδ ) σ *( ) 0 λ σ ε + σ δ = 3 b λ * ( λ ' λ*)( σ ε + σδ ) σ 0 = Sine b λ * σ > 0, it follows that 3 λ ' has to be greater than λ *. More forally, we an show that differentiation on equation B, we get: * λ σ is negative. Applying ipliit b λ b λ λ bλ b λ λ ( + ) = σ σ σ ε σ δ σ λ σ σ 3 3 b λ b λ λ = = 3 σ b λ bλ b b λ 6 σ 4 ( ) 6 ( ) + σ + σ ε + σ δ σ + σ ε + σ δ λ The last equality follows beause b is zero when λ is hosen to axiize b. It λ λ is lear that σ is negative, therefore, the optial λ dereases in σ. This result indiates that the optial λ when inentive unertainty is present is lower than the optial λ douented in Dye and Sridhar [004]. Ignoring the unertainty in anageent reporting inentives ay ause λ to be set higher than equilibriu and redue the inforational value of aounting reports. 47

58 C: Proof of inreasing loal easure of strategi dependene with inentive unertainty Reall that the best response funtions for the anager and investors are: bλ θ * ( b) = * σ b ( θ ) = σ λ σ λ σ λ σ θ ω ω + ε + (1 ) δ + The slopes of the best response funtions at the equilibriu an be obtained by taking derivative with respet to the arguent of eah equation, and then evaluating the derivatives at the equilibriu values. * θ λ θre, b = RE b * b θλ σ σ b λ σ θ σ + λ σ + λ σ + λ σ θ σ 3 3 ω = = θre, b RE θre,, ( (1 ) ) b RE θre b RE ω ε δ ω To show that the loal easure of the degree of strategi dependene is inreasing in σ, it is equivalent to show * * θ b RE, bre RE, bre b θ θ θ is inreasing in σ. Sine * θ RE, bre b θ is independent of σ, we only need to onsider * b θ θre, bre, or siply *3 b σ, as a funtion of σ. ( b σ ) b *3 * * *3 = 3b σ + b σ σ * b σ an be derived by using ipliit differentiation on equation B1 with respet to σ as follows: 48

59 Sine we get: b b λ b b λ b b σ + 3 σ + + λ σ + (1 λ) σ = 0 * * 4 * *3 4 * * ω ε δ σ σ σ σ * b σ *3 4 b λ = b λ σ σ λ σ λ σ * 4 ω + 3 (1 ) + ε + δ * b is at the equilibriu value, using equation B1 to siplify the expression, * b σ *4 4 b λ = *3 4 b λ σ + σ ω Plug it into *3 ( b σ ) σ, *3 ( b ) σ *3 = b = b *3 σ *4 4 b λ = 3b + * *3 σ b *3 4 b λ σ + σ ω *3 4 b λ 3 σ (1 ) *3 4 b λ σ + σ ω *3 4 b λ σ ω σ ( ) *3 4 b λ σ + σ ω Therefore, to show b σ *3 ( ) σ is positive, we only need to show the nuerator is *3 4 b λ greater than zero, i.e. σ ω is greater than σ. This follows easily fro equation 49

60 B1. Sine *3 4 b λ σ * * * (1 ) + b σ ω + b λ σ ε + b λ σ σ δ = ω and b σ + b λ σ + b (1 λ) σ is stritly greater than zero, it follows that * * * ω ε δ σ ω is greater than *3 4 b λ σ. D: Proof of inreasing strategi dependene with weight To show that the produt of the two best response funtions at equilibriu is inreasing in λ, it is equivalent to show * * θ b θ RE, bre RE, bre b θ θ is inreasing in λ. Fro Appendix I.C., we know θ b b θ b λ σ σ * * 3 4 = θre, bre θre, bre θre, bre ω and b 3 3 ( b λ ) λ = 3b λ + 4b λ. λ Plug 3 3 b λ bσ 4 ( ) b b δ σ λ σ ε + σ δ = λ b λ σ σ λ σ λ σ 4 ω + 3 (1 ) + ε + δ into above equation: λ 3 4 ( b ) λ b λ b λ 6λσ 1 σ 6 λ ( σ σ ) 4σ 1 σ 4λ σ 4(1 λ) σ 3 3 = b λ 4 b λ σ ω + 3 σ (1 ) + λ σ ε + λ σ δ 3 3 λσ δ λ ( σ ε + σδ ) + σ ω + σ δ = b λ 4 b λ σ ω + 3 σ (1 ) + λ σ ε + λ σδ σ + ( λ λ ) σ λ σ 4 4 δ ε + δ + ω + + ε + δ 3 3 ω δ ε = b λ 4 b σ ω + 3 λ σ (1 ) + λ σ ε + λ σδ The loal easure of strategi dependene would be inreasing in λ if 50

61 σ + ( λ λ ) σ λ σ is positive. Sine ω δ ε suffiient ondition is λ λ is always positive, a σ ε σ ω λ σ ε > 0, whih iplies a suffiient ondition is σ ω >. This ondition an also be expressed as σ >. The ratio ε σ ω σ σ ε ω indiates the relative noisiness of the anager s signal. The ore noise the anipulable signal ontains and the less variability the value of net assets has, the higher the ratio. The result indiates that the degree of strategi dependene inreases with the relative inforativeness of the anager s signal. Intuitively, the ore inforative the anager s signal, the higher the investors should rely on the aggregated report in equilibriu. Therefore, an inrease in the weight on the anager s report inreases the sensitivity of investors reliane to the anager s anipulation. E. Analysis on investors equilibriu welfare in relation to weight and inentive unertainty I first show how investors equilibriu welfare hanges with weight. The investors welfare at the equilibriu is: E V E br ω [ inv ] = [ ( ) ] bλ = E[ ( b( ω + λ + λε + (1 λ) δ ) ω) ] bλ = E b λ + λε + λ δ b ω bλ = b + + Take derivative with respet to λ : [( ( (1 ) ) (1 ) ) ] [( ) σ λ σ ε (1 λ) σ δ ] (1 b) σ ω 51

62 E[ Vinv ] λ b bλ = + + λ 3 b λ b [ σ + λσ ε (1 λ ) σ δ ] 3 bλ b b λ = b( ) σ b [ σ + λ( σ ε + σ δ ) σ δ ] λ [ ( b( ) σ bλ σ ε b(1 λ) σ δ (1 b) σω )] Sine 3 3 b λ bσ 4 ( ) b b δ σ λ σ ε + σ δ = λ b λ σ σ λ σ λ σ 4 ω + 3 (1 ) + ε + δ holds in equilibriu, the above equation an be written as: E[ Vinv ] λ 4 bλ b b λ b = b( ) σ + b[ σ ω + 3 σ (1 ) ] + λ σ ε + λ σδ λ λ 4 b λ b = b[ σω + σ (1 ) ] + λ σ ε + λ σδ λ b = σ ω λ The last equality oes fro the equilibriu b being σ ω. Sine bλ σω + λ ( ) σ + λ σ ε + (1 λ) σδ E[ V inv ] λ has the sae sign as b λ, when b λ is hosen to axiize b, i.e. = 0, investors welfare is also axiized. λ Now I show investors equilibriu welfare dereases in inentive unertainty. Take derivative with respet to σ : 5

63 E[ V ] σ inv b bλ b λ = [ ( ( ) + + (1 ) + )] σ 4 4 b σ bλ σ ε b λ σ δ bσ ω σ ω b bλ b λ = [ ( ( ) + )] σ 4 4 b σ σ ω σ ω bλ b b λ = b( ) 4 4 σ σ 4 4 b λ 4 4 bλ ( ) b λ = b σ 3 4 b λ σ + σ ω 4 4 b λ σ ω = 3 4 b λ σ + σ ω Sine 4 4 b λ σ ω is always negative, it shows investors welfare dereases with the unertainty in anageent reporting inentives. F. Proof of the optiality of a linear valuation odel bλ Fro Appendix I.A., we know r = ω + λ( + εω ) + (1 λ) δ. ω,, ε ω, and δ are independently and norally distributed. Therefore, (r, ω ) are bivariate noral. Speifially, (r, ω ) ~ bivariate noral ( µ, µ, σ, σ, ρ ), where r ω r ω rω bλ µ r = ω +, µ ω = ω, bλ σ r = σω + λ ( ) σ + λ σ ε + (1 λ) σδ, σ = σ, and ω ω 53

64 ρ rω σ ω =. bλ σω σω + λ ( ) σ + λ σ ε + (1 λ) σδ Given the norality assuption, the best preditor of ω given investors quadrati loss funtion is siply E[ω r]. σ ω ωe =E[ ω r]=( µ ρ µ ) + ρ σ ω ω rω r rω r r σ r σ ω bλ = ω + ( r ω ) bλ σ ( ) (1 ) ω + λ σ + λ σ ε + λ σ δ This proves that the best valuation funtion is linear in r. Moreover, when ω and σ r are zero, E[ω r] is siplified to σ ω r. bλ σω + λ ( ) σ + λ σ ε + (1 λ) σ δ The variane of the best preditor is Var ω r σω ρ ω ( e ) = (1 r ) bλ σ ω ( λ ( ) σ + λ σ ε + (1 λ) σδ ) = bλ σ + λ ( ) σ + λ σ + (1 λ) σ ω ε δ 54

65 II: Instrutions Introdution This experient is about eonoi deision aking. You will be paired with another subjet to play a two-person gae for 10 rounds per senario in any different senarios. Soe senarios ay be played ultiple ties, while soe other senarios will only be played one or not at all. You will always know whih senario you are in. There are 64 rounds in total inluding 4 pratie rounds. At the end of the session, we will ask you a series of questions about your experiene. The total session lasts about 80 inutes. You will gain laboratory dollars in this experient. Your gains in laboratory dollars will be onverted to US dollars after you oplete the experient. Overview There are two types of players: reporter and appraiser. Half of the subjets will be randoly piked to play the role of reporter and the other half will play the role of appraiser for the entire session. A reporter will be randoly paired with an appraiser at the beginning of the session and will play with the sae appraiser throughout the session. Players identities are kept anonyous throughout the experient. The reporter learns a base value, and reports a nuber to the appraiser. The appraiser estiates the base value based on the reported nuber. The appraiser always earns ore by estiating the base value ore aurately. The reporter soeties earns ore by getting the appraiser to overestiate the base value, and soeties earns ore by getting the appraiser to underestiate the base value, depending on a rando nuber alled an inentive ultiplier. Reporter s Task The base value is a rando variable with ean zero and standard deviation 10. The inentive ultiplier indiates how his/her payoff will be linked to the appraiser s 55

66 estiate of the base value. The standard deviation of the ultiplier will be different in different senarios. A higher standard deviation eans the realized inentive ultiplier is ore likely to be farther away fro zero. The reporter s task is to hoose an adjustent fator whih will be ultiplied with the inentive ultiplier to deterine the reporter s total adjustent for eah report. The perentage of the adjustent that is added to base value will be different in different senarios. A higher weight on the total adjustent eans the reported value is influened ore by the reporter s adjustent. In suary, the report is deterined by the equation: Reported Value = Base Value + Weight x (Inentive Multiplier x Adjustent Fator) If the reporter hooses an adjustent fator of 0, the reported value is always equal to the base value. Greater adjustent fators ake the report lower than the base value if the inentive ultiplier is negative. Greater adjustent fators ake the report higher than the base value if the inentive ultiplier is positive. The greater the adjustent fator, the ore the report is inreased (for positive inentive ultipliers) or dereased (for negative inentive ultipliers), other things equal. The reporter is also harged a fee for the total adjustent. The fee inreases with the total adjustent. 100 Reports in Eah period Rather than hoose a different adjustent fator every tie, reporters hoose a single adjustent fator that is applied to 100 different reports. Every report has its own randoly-hosen base value and its own randoly-hosen inentive ultiplier. Your oputer sreen will show the average payoff for the entire set of 100 reports. 56

67 Appraiser s Task The appraiser s task is to estiate the base value for eah report as aurately as possible. Speifially, the appraiser is harged based on the square of the differene between the estiate and the base value. For exaple, if the appraiser estiates a value of 14, and the base value is 9, the harge will be (14-9) = 5. Instead of hoosing different estiate for eah report, the appraiser hooses a single nuber, alled reliane, to oe up with an estiate. For eah report, the appraiser s estiate is deterined by this equation: Appraiser s Estiate = Reliane x Reported Value If the reporter has hosen an adjustent fator of 0, the appraiser s best hoie is selet reliane of 100%, beause the report is exatly equal to the base value. The higher the reporter s adjustent fator, the less reliant the appraiser should be, beause high reports probably indiate that the reporter adjusted upward, and low reports probably indiate that the reporter adjusted downward. Payoff Calulation The reporter s laboratory payoff for eah round is the average payoff of all 100 reports. The reporter s laboratory payoff for eah report is deterined by the equation: Reporter s Payoff = Inentive Multiplier x Appraiser s Estiate Cost of Adjustent The appraiser s laboratory payoff for eah round is also the average payoff of all 100 reports. The appraiser s laboratory payoff for eah report is deterined by the equation: Appraiser s Payoff = (Appraiser s Estiate Base Value) Your sreen shows the average expeted payoff alulated based on your expetation of the other player s strategy and on your own hoie in the sae way as the atual payoff alulation of all 100 reports (shown in yellow at the botto of your 57

68 deision aking sreen). You an use the dropdown enus to selet different obinations of the other player s strategy you expet and your own strategy to see how your expeted payoff is affeted. However, your expeted payoff is alulated based on your expetation of the strategy of the other player, whih ay deviate fro the atual strategy played out by the other player that deterines your atual payoff. Converting laboratory payoffs into US dollars Your total laboratory payoffs will be onverted into US dollars aording to the following onversion rule: USD Winnings = Exhange Rate x (Your Laboratory Payoffs + Adjustent ) You will not learn the exat exhange rate and adjustent. However, there are a few fats you an learn. First, the exhange rate is positive, eaning that the ore laboratory dollars you win, or the fewer you lose, the ore USD you get. Seond, the exhange rate is set to be independent of the perforane of the other player in your pair. Third, adjustent will be different for reporters and appraisers. The exhange rate and adjustent are set so that the average winnings will be approxiately US$5 for eah person for the session. You will also reeive $5 in ash for partiipation when you finish the experient. Suary The flow of inforation and deision aking is suarized in Figure 1 below: Figure 1: Flow of Inforation and Deision Making Base Value Reporter's Adjustent Reported Value Appraiser's Estiate Payoffs Reporter's Inentive Weight Appraiser's Inentive 58

69 III: Sreen Shots A. Deision sreen for investors 59 B. Deision sreen for anagers