Is Reputation Good or Bad? An Experiment

Transcription

1 Is Reputation Good or Bad? An Experiment By Brit Grosskopf and Rajiv Sarin November 08, 2009 We investigate the impact of reputation in a laboratory experiment. We do so by varying whether the past choices of a long run player are observable by the short run players. Our framework allows for reputation to have either a bene cial or a harmful e ect on the long run player. We nd that reputation is seldom harmful and its bene cial e ects are not as strong as theory suggests. When reputational concerns are at odds with other regarding preferences, we nd the latter overwhelm the former. (JEL C70, C91) A central concern of many long lived agents is their reputation. A doctor, who hopes to treat many di erent patients over her career, and whose treatments are observed by potential future patients, needs to be concerned Grosskopf: Department of Economics, Texas A&M University, TAMU 4228, College Station, TX ( bgrosskopf@econmail.tamu.edu); Sarin: Department of Economics, Texas A&M University, TAMU 4228, College Station, TX ( rsarin@econmail.tamu.edu). This paper has bene ted from comments from audiences at the Brown Bag Seminar at Texas A&M University and seminars at the following universities: Alabama, Arizona, Charles (CERGE), Laval, New York, Pittsburgh, Pompeu Fabra, Technical at Berlin, Texas at Dallas, Queen Mary, Victoria at Wellington, and the Max Planck Institute of Economics. We also acknowledge insightful audiences at the following meetings: Econometric Society (Chennai and Pittsburgh), Economic Science Association (Tucson and Rome), Game Theory Society (Stony Brook and Evanston), Society for the Advancement of Economic Theory (Vigo), SITE and the First Singapore Economic Theory Workshop. We are indebted to Vince Crawford and two anonymous referees whose comments have greatly improved the paper. We thank Paan Jindapon and Elizabeth Watson for indispensable help in running the experimental sessions. Financial support from NSF SES# is gratefully acknowledged. 1

2 about the reputation she has for providing quality healthcare. Without such a reputation the doctor may not be visited by many patients. An entrepreneur, who needs loans from many, possibly di erent, nancial institutions over time, ought to be concerned about whether she has a good credit history and hence a reputation for paying back loans promptly. In the absence of such a reputation the entrepreneur may not obtain the loans she requires to meet her current needs and hence may face bankruptcy. Similarly, a retailer who serves many consumers over time needs to be concerned about whether she has a reputation for providing quality service. Without it, potential customers might go to her competitors. A suitable reputation may play an important role in the success of a long lived agent, whatever her objectives. The seminal work on reputation of David Kreps and Robert Wilson (1982) and Paul Milgrom and John Roberts (1982) considers a long run player who meets a sequence of short run players who are unsure about the long run player s preferences but observe her previous choices. Through the observability of her previous choices the long run player establishes a reputation about her preferences or type. This work suggests that the ability to have a reputation could allow the long run player to obtain higher payo s than would be available to her otherwise. 1 That is, reputation is good for the long run player. An entrepreneur (long run player) may bene t from having a credit history when seeking a loan from a lender (short run player). Intuitively, a suitable credit history gives the potential lender con dence that the loan will be repaid and this serves the entrepreneur s interests. But, is having a reputation necessarily bene cial for the long run player? Should a doctor reveal what treatments she has given to past patients? Should a car mechanic reveal what repairs she has performed on previous automobiles brought to her shop? Recent work by Je rey Ely and Juuso Valimaki (2003) suggests that the observability of past actions might actually lower the long run player s payo s. That is, reputation is bad for the long run player. They show that a doctor, whose preferences coincide with that of a patient, may choose a treatment that is harmful to the patient in order to enhance her reputation with potential future patients. Roughly speaking, this happens because prescribing a speci c treatment might enhance a doctor s reputation independent of its suitability for the current patient. 1 Drew Fudenberg and David K. Levine (1989, 1992) provide precise bounds on how much a reputation could bene t a long run player. 2

3 Consequently, potential patients may avoid a doctor with reputational concerns whereas they would have chosen to visit her had such concerns been absent. The objective of this paper is to experimentally investigate the impact of reputation. To do this we vary whether the past choices of a long run player are observed by the short run players. We develop a framework, which we call the Bad Framework, that allows us to test whether reputation is bad for the long run player. A specialization of this framework, which we call the Good Framework, allows us to test if reputation is good. Our analysis provides a rst experimental test of the bad reputation prediction and also a rst test of the, now classic, prediction that reputation is bene cial for the long run player. Our study, additionally, reveals the factors which distinguish situations in which reputation may be bad from those in which it can be good. Roughly speaking, reputation may be bad if short run players can entertain some doubt about the suitability of the action chosen by the long run player. When such doubt is not possible, reputation can be good. Observing the treatment a doctor provides may not identify her type whereas observing that an entrepreneur has previously reneged on a loan unambiguously identi es her type. 2 We obtain two surprising results. First, reputation is seldom harmful. In the Bad Framework, long run players whose past choices are observed earn more than those whose past choices are not observed. Second, the bene t a long lived player obtains from providing information on her past actions may not be as large as theory suggests. This is because long run players, in the Good Framework, whose past choices are not observed do not earn less than those whose choices are observed. Both these results can be explained by the willingness of short run players to interact with the long run player when theory predicts otherwise. To provide insight into what drives the willingness of short run players to interact with the long run player we design a suitable Dictator like game in which the Dictator s choice mimics the choice faced by the long run player if given a loan. We use this game to study the Dictator s choice and to elicit the Receiver s belief regarding this choice. The choices of the Dictators 2 A recent study that investigates the conditions under which reputation may be bad is Ely, Fudenberg and Levine (2008). 3

4 reveal their preference to often choose according to the Receivers interests (i.e., choose appropriately). Although they underestimate the extent, Receivers anticipate appropriate choices from Dictators. These ndings suggest that short run players may be willing to interact with the long run player because they correctly believe that the long run player will often choose appropriately. 3 Consequently, the additional bene t of providing information about past choices, in the Good Framework, is not as pronounced as theory predicts. Using the revealed preferences of the long run players and the expectation thereof, we cannot, however, explain why short run players interact with them in the Bad Framework. Given our design of this framework, even the slightest amount of inappropriate behavior by the long run players should lead the short run players to withdraw from participating in the market. Since we nd some inappropriate behavior, and as more seems to be expected, the persistent market participation of short run players reveals that they themselves may be guided by preferences for appropriate choices (i.e., choices bene cial to the long run player). Our work suggests that the bene t some borrowers obtain from having a good credit history may not be as large as previously thought. Lenders may o er loans simply because they believe borrowers care about repaying them. Our ndings also suggest that patients may visit a doctor even when her past choices are observable. The tendency of the players to choose appropriately prevails over the market destroying e ect of reputation. Taking the results in the Good and Bad Framework jointly, our experiment, suggests that the predictions of theory are less likely to be refuted when they prescribe appropriate choices. Our study reveals the tendency of both, the long run and the short run, players to take the concern of other players into account. This implies that models incorporating other regarding preferences (e.g., Ernst Fehr and Klaus Schmidt, 1999, and Gary E. Bolton and Axel Ockenfels, 2000) would be useful to study questions of reputation. This is especially important when other regarding preferences and reputational concerns predict distinct and potentially opposing behavior as they do in the Bad Framework. 4 3 Such an e ect was referred to as homemade priors by Colin Camerer and Keith Weigelt (1988) to explain systematic deviations from sequential equilibrium predictions. 4 John A. List (2006) argues that reputational concerns substitute for other regarding 4

5 Camerer and Weigelt (1988) is the rst study to design an experiment with a long run player interacting with a sequence of short run players who are unsure about her preferences and observe her previous choices. The stage game they study is a Trust game with incomplete information about the Trustor, which is a special case of the game we develop in this paper. 5 Camerer and Weigelt (1988), like the follow up studies of John Neral and Jack Ochs (1992) and Jordi Brandts and Neus Figueras (2003), focus on how sequential equilibrium predicts behavior. Camerer and Weigelt s design varies the probability with which the long run player is of either type but does not vary the information available to the short run players. None of these papers vary the observability of past choices of the long run player and, hence, none of them study the impact of reputation. A study that varies the availability of information regarding the long run player s choices is Bolton, Elena Katok and Ockenfels (2004). They allow buyers (short run players) to observe or not the previous choices of sellers (long run players). They nd that reputation helps the long run players realize higher payo s. The stage game they study is a variant of the Trust game. Their setting is di erent from ours and Camerer and Weigelt s in that the buyers have no uncertainty about the sellers preferences. Uncertainty regarding these preferences is a critical part of classic reputation models. Another related study is Vital Anderhub, Dirk Engelmann and Werner Güth (2002). The stage game they study is the Trust game in which the Trustor has incomplete information about the Trustee s preferences. In their study both players are long lived and play a repeated Trust game under incomplete information. The study of reputation when both players are long run is distinct from what we investigate in this paper. This paper is organized as follows. In the next section we present our experimental design. Section II derives the theoretical predictions. Section III reports the experimental ndings. Section IV discusses some of the salient and surprising features of these results. Section V concludes. The Appendix presents details of the Probit estimations. The web Appendix contains additional data and a sample set of Instructions. preferences in the marketplace. His argument refers to the Good Framework in which they both predict the same behavior. 5 For the canonical Trust game, see Joyce Berg, John Dickhaut and Kevin McCabe (1995). 5

6 I. Experimental Design A long run player, called the entrepreneur, meets a sequence of six short run players, called banks. The entrepreneur s preferences are unknown to the banks. Banks know that there are two types of entrepreneurs: friendly and unfriendly, with each type being equally likely. A friendly entrepreneur has preferences which are aligned with those of the banks whereas an unfriendly entrepreneur does not. The stage game of this interaction is illustrated in Figure 1, in which a bank (entrepreneur) is referred to as a B (E) player. Figure 1: The reputation stage game 6

7 Each of the banks that an entrepreneur meets has to decide whether or not to give her a loan (i.e., choose b2 or b1). If a bank refuses to give a loan then the interaction with the entrepreneur ends. If a loan is given, the entrepreneur has to choose a project (e1 or e2). Which project is appropriate (i.e., maximizes the bank s payo ) is potentially unknown to the banks but known by the entrepreneur. The appropriateness of the project is determined by the state of the world, which may be either N or P. Our design varies whether the entrepreneur can have a reputation or not by varying whether her past choices are observed by banks. In the treatments in which the previous choices of an entrepreneur are not observed, each of the six meetings between an entrepreneur and a bank are unrelated. 6 Our design also varies the probability with which a project is appropriate. In the treatments in which reputation is predicted to be bad, each project is appropriate with equal probability (i.e., Pr (N) = Pr (P ) = 1=2). Reputation is predicted to be good when a speci c project (e1) is always appropriate. This happens when Pr (P ) = 1. 7 We refer to treatments in which Pr (N) = Pr (P ) = 1=2 as the Bad Framework and those in which Pr (P ) = 1 as the Good Framework. Our 22 experimental design is summarized in Table I. Table I: The 22 Experimental Design w/ Reputation w/o Reputation Bad Framework 4 sessions 4 sessions Good Framework 4 sessions 4 sessions To isolate the e ect of reputation, and to make sharp predictions, models that study the impact of reputation (e.g., Kreps and Wilson, 1982) assume that speci c types of a long run player are committed to choose particular 6 Hence, referring to the entrepreneur as a long run player in these treatments involves an abuse of terminology. 7 In this case, our experimental design collapses to that designed and tested by Camerer and Weigelt (1988). We have changed the payo s in comparison to that study in order to avoid the possibility of negative payo s and to have simpler numbers for the subjects. This also enabled us to keep the same exchange rate from points to dollars for subjects in di erent roles. 7

8 actions. We implement committed players through computerized players who are programmed to always choose a speci c action. Using computerized players removes the possibility of decision making errors on the part of (human) subjects, the possibility that they are guided by non monetary concerns and the anticipation of such e ects by other players. Hence, using computerized subjects allows for a better test of the theory. It also helps reduce both the number of subjects needed to run a session and subject payments. In accordance with theory, we computerize the manner in which the unfriendly entrepreneur chooses in the Bad Framework (always e2). In the Good Framework we computerize the choices of the friendly entrepreneur (always e1). We use a between subject design, i.e., each subject participates only once in our experiment. We run 4 sessions of each treatment. Each session consists of nine human participants. Six of them are randomly determined to be banks and the remaining three are entrepreneurs. Participants remain in their respective roles throughout a session. Additionally, there are three computerized entrepreneurs. 8 All subjects are aware of the existence of the computerized players. 9 We refer to the game in which one entrepreneur meets with six di erent banks as a sequence. In any session, six entrepreneurs are concurrently playing. Hence, we have six sequences that are concurrently played. Each entrepreneur plays 10 sequences. 10 The banks and entrepreneurs are distinguished not only by the choices they have to make but also by the information they have about one another. Entrepreneurs never obtain any information on the earlier choices of the bank they are meeting or about the decisions of any of the other entrepreneurs. Banks, however, know the previous choices of the entrepreneur they are meeting in the treatments in which reputation is possible. 8 See Brit Grosskopf and Rajiv Sarin (2008) for implementations with other than proportions of the two di erent types of entrepreneurs and for implementations without computerized players. 9 Active computer terminals were situated between subjects. Participants were informed about this. No participant seemed confused about the existence and strategy of the computerized players. 10 The matching of participants in the six concurrently played sequences can be thought of as a 6 6 matrix where the rows indicate the rounds and the columns refer to the IDs of the entrepreneurs. An individual bank can only appear once per row and column. Ten of these matrices were randomly generated in advance. 8

9 Entrepreneurs meet banks in a randomly predetermined order that changes from sequence to sequence. The state of the world is determined independently for each entrepreneur before each meeting with a bank. Whereas entrepreneurs know their own preferences and the state of the world, banks only know the number of entrepreneurs of each type and the probability of each state of the world. All players are informed about this. The states of the world are randomly generated in advance and kept xed for the Bad Framework sessions. Our design modi es that used in previous experimental studies in which a long run player interacts with a sequence of short run players who are uncertain about her preferences (Camerer and Weigelt, 1988, and Brandts and Figueras, 2003) in several ways. First, in contrast to these studies, we use computerized players to implement committed types. Second, we have entrepreneurs and banks concurrently playing the game. This allows us to (i) virtually eliminate the need for players to wait while other players make decisions, 11 while allowing us to collect more data per session, (ii) limit the amount of information that players get about the choices of other players in the same role and the choices of other players in a di erent role with whom they are not paired. In particular, our design restricts any population type learning which could have occurred in the experiments of Camerer and Weigelt (1988) and Brandts and Figueras (2003). In these papers, all entrepreneurs see the choices of the one entrepreneur that is randomly selected to be the long run player for the current sequence and the corresponding choices of banks. In both these studies the type of the entrepreneur was revealed to the banks at the end of the sequence. Our banks are never informed about the type of the entrepreneur with whom they were interacting. Hence, our study also reduces the learning between sequences. All sessions were conducted at the Economic Research Laboratory at Texas A&M University, from June 2004 until November Participants were undergraduate students of all, but economics, majors. The computer interface was programmed using z Tree (Urs Fischbacher, 2007). The participants were not allowed to communicate with one another and dividers separated the individual computer terminals. Instructions were read aloud 11 This was present in the earlier literature and resulted in boredom e ects. These e ects have been considered a shortcoming of the earlier designs. 9

10 and questions answered in private. 12 After reading the instructions and having questions answered, all participants had to answer a set of questions that were meant to test whether the instructions had been understood. All answers were individually checked and corrected by the experimenters and any remaining questions were answered. An experimental session typically lasted about two hours. Participants were given a score sheet to record their choices and earnings for the entire session. They were paid their accumulated earnings at the end of the session. Payo s in points were converted to dollars at the rate of 1 point = $0.12. Average earnings were $ An additional $5 show up fee was paid. The instructions did not mention any frame or context. The bank entrepreneur frame we provide in the text seeks to make our discussion more easily comparable with the earlier literature. We supplement the above sessions with data from one shot decisions in which 34 students (who had not previously participated) took part in a pen and paper experiment in October Half of them were randomly chosen to be Dictators and the others were Receivers. After initially meeting in the same room and going over the instructions, Dictators and Receivers were separated into two rooms. Dictators had to make six choices which determined their own payo and that of the Receivers with whom they were paired. The results of one of the six decisions are discussed later in the paper. Instructions can be found in web Appendix C. Two of the six choices were randomly selected to be paid. We paid a $7.50 show up fee for this much shorter experiment in which the average earnings were $15.26 including the show up fee. II. Theoretical Predictions A. Bad Framework A friendly entrepreneur, in the Bad Framework with reputation, has no reputational concerns in the last (sixth) round. Hence, if given a loan, she chooses e2 if the state of the world is N and e1 if the state of the world is P. Consider the strategy of a bank in the sixth round. If he observes that the entrepreneur has previously chosen e1 then he knows the entrepreneur is friendly and has interests aligned with his. He should choose b2 and get a payo of 4. If the entrepreneur he meets has never chosen e1 but has sometimes chosen e2 then the updated beliefs of the bank are such that he 12 A sample set of instructions can be found in web Appendix B. 10

11 believes the entrepreneur is friendly with strictly lower than 50% probability and hence the bank gets a higher payo from choosing b1. If the entrepreneur has never previously been given a loan then the bank is indi erent between b1 and b2. Given the strategy of the bank in the last round, we can calculate the strategy of the entrepreneur in the penultimate round. If she has never previously been given a loan then she should choose e1 if given a loan, independently of the state of the world. To see this note that she obviously chooses e1 if the state of the world is P. If the state is N then she gets a payo of 4 in the current round from choosing e1 and an expected payo of 4.5 in the nal round whereas she would obtain 5 in the current round and 3 in the last if she chooses e2. 13 If she has previously been given a loan then her optimal response depends on her previous choice(s). If she has previously chosen e1 then she should choose the appropriate action (e2 if state N and e1 if state P ). If she has never previously chosen e1 but only chosen e2 then she should not have been given a loan. This is, hence, o the equilibrium path and we assume she chooses e1, independently of the state, in order to ensure that she gets a loan in the nal round. The optimal response to the entrepreneur s strategy in the 5th round is for the bank to choose b2 if the entrepreneur has previously chosen e1 and to choose b1 otherwise. The equilibrium unravels. In round 1 the entrepreneur chooses e1 regardless of the state and the bank chooses b1. Hence, there is no market interaction except possibly in the last round. O the equilibrium path, we suppose for the friendly entrepreneurs that Prfe1jb2 ^ t < 6 ^ no previous e1g = 1, and for banks that Prfb2je1 in any previous roundg = 1. Given the strategies above, banks have a per round expected payo of 3. Entrepreneurs obtain 3 in the rst 5 rounds and obtain an expected payo of 4.5 if given a loan in the last round and 3 if not given a loan. As the bank is indi erent between giving a loan or not in the last round, the expected per round earnings of the entrepreneur lie in the interval [3; 3:25]. In contrast, without reputational concerns the friendly entrepreneur will always choose the appropriate project. Consequently, a bank s expected 13 As is common in the analysis of such games, we assume risk neutrality, additive utility and no discounting of future payo s. 11

12 payo from giving a loan is 3 which is what he obtains from not giving a loan. Expected payo s of the entrepreneur, therefore, are predicted to lie in the interval [3; 4:5]. As banks are indi erent between giving a loan and not, it seems reasonable to suppose that they give a loan 50% of the time. If this is the case the friendly entrepreneur will earn 0:53+0:5(0:55+0:54) = 3:75 per round. Reputation is bad in this framework because the entrepreneur obtains a lower payo when her past actions are observed in comparison to when they are not observed. Predicted choices of banks and entrepreneurs as well as their expected earnings in the Bad Framework are given in Table II. Table II: Summary of the Theoretical Predictions (Bad Framework) 14 w/ Reputation w/o Reputation R1 R2 R3 R4 R5 R6 Average Each round Choices P rfb2g [0; 1] [0; 1] P rfe1jn g Earnings Banks Entrepreneurs [3; 4:5] [3; 3:25] [3; 4:5] B. Good Framework In the Good Framework with reputation an unfriendly entrepreneur in the last (sixth) round has no reputational concerns. Hence, if given a loan she chooses e2. Consider the strategy of a bank in this last round. If he observes that the entrepreneur has previously chosen e2 then he knows the entrepreneur is unfriendly. He should, therefore, choose b1. Even if the entrepreneur has never previously received a loan the bank should choose b1. If the entrepreneur has never chosen e2 but has sometimes chosen e1 then the updated beliefs of the bank have to take into account that an unfriendly entrepreneur might have strategically chosen the appropriate 14 R# refers to round #. Choices are in probabilities and earnings are in points. 12

13 project (e1) in previous rounds. Let s assume that in the nal round T the bank believes the entrepreneur is friendly with probability p T. Then, the bank should choose b2 if 4p T > 3. This means that as long as the entrepreneur s reputation, measured by p T, is greater than the threshold of, the bank will choose b In round T 1, an unfriendly entrepreneur who is given a loan has two choices. Either she could choose e2 and get 5 and another 3 in T or she can play a mixed strategy, choosing e1 with probability s T 1. The entrepreneur s total expected earnings from rounds T 1 and T are (4 + 5)s T 1 + (5 + 3)(1 s T 1 ) = s T The entrepreneur will want to choose s T 1 as large as possible so that when a bank observes her choice of the appropriate project (e1) in round T 1 and updates his beliefs about the entrepreneur s type, his updated posterior probability p T is above the threshold of 3. If 4 the probability p T is exactly at this threshold, the bank will be indi erent between lending and not lending. The bank will choose a mixed strategy probability which makes the entrepreneur indi erent between choosing e1 and e2, and the entrepreneur will choose a mixed strategy probability which makes the posterior probability p T equal to its threshold. If the bank uses Bayes rule to update probabilities, the posterior probability p T is given by p T = p T 1 =(p T 1 +s T 1 (1 p T )). For this posterior p T to exceed the lending threshold of 3 requires s 4 T 1 < 1 p T p T 1. The entrepreneur will choose s T 1 to make this hold with equality. In round T 1, a bank will choose b2 if and only if his expected payo from lending is greater than his expected payo from not lending. That is, 4(p T 1 + s T 1 (1 p T 1 )) > 3. Since the entrepreneur will choose s T 1 = 1 p T p T 1, we nd the bank s lending threshold in round T 1 to be p T > 4 3 In h round it k, the entrepreneur s mixed strategy should satisfy s T k = 4 k 3 1 pt k k+1. 1 p T k and the bank s lending threshold is p T k > 4 3 This threshold is smaller in earlier rounds because even unfriendly entrepreneurs are likely to choose the appropriate project initially. Therefore, banks require less assurance that the entrepreneur is friendly to convince them to lend. Since each sequence begins with the commonly known prior of 0.5, in every sequential equilibrium a bank lends and the unfriendly entrepreneur chooses the appropriate project, as long as the prior of 0.5 is above the threshold of 3 k+1(with 4 k = 5 in the rst round). As k gets smaller, the threshold goes up. In the round before the threshold is supposed to be higher than 0.5, 13

14 the entrepreneur has to do something to enhance her reputation that is, to increase the bank s posterior probability that the entrepreneur is friendly or else the bank would refuse to lend in the remaining rounds. That is why the entrepreneur starts mixing in the last round when the bank is still giving a loan for sure. With the choice of our parameters this happens in round 4 and we get a probability for choosing the inappropriate project of As mentioned before, once mixed strategy play begins, the entrepreneur s choice of s T in equilibrium makes the bank indi erent between his strategies. The bank chooses to lend with probability m, where m makes the entrepreneur indi erent between mixing and choosing the inappropriate project for sure. The expected payo of the entrepreneur from mixing in round T 1 is s T 1 [4 + 5m + 3(1 m)] + (1 s T 1 )(5 + 3): Setting this equal to 8 (5 in round T 1 and 3 in round T ), which is the expected payo from choosing the inappropriate project, gets us a value of m that is equal to 0.5. This mixing probability is optimal in every round where the posterior probability p T k equals the bank s threshold. We assume the o equilibrium beliefs of a bank are such that if he observes the entrepreneur has previously chosen e2 then he is convinced that the entrepreneur is unfriendly. Hence, we assume Prfb1je2 in t < 4g = 1. Table III: Summary of the Theoretical Predictions (Good Framework) w/ Reputation w/o Reputation R1 R2 R3 R4 R5 R6 Average Each round Choices P rfb2g P rfe2g Earnings Banks Entrepreneurs If reputation building is not possible, the unfriendly entrepreneur should always choose e2 and, hence, the banks should always choose b1. There is 14

15 no market interaction. The long run player is predicted to receive a payo of 3. Reputation is good in this framework because the long run player is predicted to earn more in the treatment in which reputation building is possible in comparison to when it is not possible. Predicted choices of banks and entrepreneurs and their expected earnings in the Good Framework are given in Table III. III. Experimental Results If reputation is bad (good), the earnings of entrepreneurs whose past choices are observed should be lower (higher) than the earnings of those whose past choices are not observed. We begin, in subsection A, by reporting earnings. This allows us to ascertain the e ects of reputation and to compare them to the theoretical predictions. To gain further insight into what is driving the reputation e ects, we focus on the behavior of banks in subsection B and on that of entrepreneurs in subsection C. A. Payo Comparisons Table IV compares the average per round earnings of entrepreneurs and banks with those predicted by theory (given in parentheses), in each of the treatments. While we report data aggregated over all sessions, any nonparametric tests are done using session level data. 15 Table IV: Per Round Earnings by Treatment (Predictions in parentheses) w/ Reputation w/o Reputation Bad Framework Banks 3.00 (3) 2.99 (3) Entrepreneurs 3.95 ([3,3.25]) 3.70 ([3,4.5]) Good Framework Banks 3.31 (3.59) 3.10 (3) Entrepreneurs 3.73 (3.86) 3.77 (3) 15 See Sidney Siegel and N. John Castellan Jr. (1988) for the nonparametric tests used in this paper. 15

16 Entrepreneurs in the Bad Framework earn signi cantly more when their past choices are observed in comparison to when they are not (Robust Rank Order test, U = 2:5022, p = 0:05). Hence, reputation in not harmful. This result is driven by the higher than predicted earnings of entrepreneurs in the Bad Framework with reputation in which each entrepreneur earns more than 3.25, the upper bound of the theoretical prediction. Earnings of entrepreneurs without reputation are in the theoretically predicted interval. Earnings of entrepreneurs in the Good Framework are not signi cantly di erent as we vary the observability of the entrepreneur s past choices (Robust Rank Order tests, U = 0, n:s:). Hence, there is no additional bene t of having a reputation in the Good Framework. This nding is driven by the higher than predicted earnings of entrepreneurs in the Good Framework without reputation in which every entrepreneur earns more than the theoretically predicted 3. The earnings of entrepreneurs do not di er from predictions in the Good Framework with reputation (Binomial test, one tailed p = 0:194). The earnings of banks do not di er signi cantly as we vary reputation building possibilities in each framework (Robust Rank Order test, Bad Framework: U = 0:5394, n:s:, Good Framework: U = 1:2649, n:s:). Banks earnings do not di er signi cantly from the theoretical predictions in the Bad Framework (Binomial test, w/ Reputation: one tailed p = 0:581, w/o Reputation: one tailed p = 0:271). Banks, in the Good Framework with reputation, do worse than predicted (Binomial test, one tailed p = 0:003), while their peers without reputation do just as well as predicted (Binomial test, one tailed p = 0:154). B. Bank Behavior In this subsection, we begin by reporting bank behavior in the rst round. We then study the manner in which banks respond to the reputation of the entrepreneur. Finally, we perform random e ects Probit estimations to control for individual heterogeneity. These estimations also control for other variables that could a ect bank behavior. Since no change in behavior is found across sequences we pool the data from all sequences See web Appendix A for the data and analysis of round 1 loan giving across sequences. 16

17 Table V reports loan giving in round 1 by treatment. Initial loan giving in the Bad Framework is marginally higher when reputation is possible than when it is not possible (Robust Rank Order test, U = 1:5861, p = 0:1). Loan giving is well above the theoretical prediction in the Bad Framework with reputation while it is consistent with the prediction in the treatment without reputation. 17 Table V: Loan Giving in Round 1 by Treatment (Predictions in parentheses) w/ Reputation w/o Reputation Bad Framework 60% 144 (0%) % 240 Good Framework 63% (100%) 60% (0%) There is no di erence between initial loan giving in the Good Framework when reputation building is possible compared to when it is not (Robust Rank Order test, U = 0:1240, n:s:). Loan giving is well above the theoretical prediction in the Good Framework without reputation while it is somewhat below the prediction in the treatment with reputation. Camerer and Weigelt (1988) and Neral and Ochs (1992) nd a much higher initial rate of loan giving in the Good Framework with reputation than we do. When 30% of the entrepreneurs are friendly they nd 96.03% (Camerer and Weigelt) and 100% (Neral and Ochs) loan giving. The high proportion of loan giving in Camerer and Weigelt could be driven by the fact that their sequence consists of 8 rounds. The Neral and Ochs result can be explained by the fact that a bank and an entrepreneur are interacting with one another for the entire duration of a sequence. Brandts and Figueras (2003) nd a much lower proportion of initial loan giving, in particular in the treatments most comparable to this study. When the proportion of friendly entrepreneurs is 50% they observe 37% loan giving in the rst round. This is lower than what we nd but their corresponding sequence length is only 17 Banks are predicted to be indi erent between giving a loan or not in the Bad Framework without reputation. Conducting Binomial tests on session level data we nd that in 2 out of the 4 sessions initial loan giving is not signi cantly di erent from 50%. 17

18 3 rounds. When the proportion of friendly entrepreneurs is 25% and a sequence consists of 6 rounds they observe 57.4% initial loan giving which is close to the 63% we obtain. Next we analyze how banks react to the reputation of the entrepreneur. Table VI shows summary statistics (aggregated over all participants, rounds and sessions) of the responsiveness of banks to the history of the entrepreneur. We include conditional loan giving information of banks in the treatments without reputation, in which they do not know the past choices of the entrepreneur, to see whether loan giving varies with the reputation of the entrepreneurs or is just random. Recall that, with reputation, the action that unambiguously identi es a friendly entrepreneur in the Bad Framework is the choice of e1. In the Good Framework it is a choice of e2 that unambiguously identi es an unfriendly entrepreneur. Observing that an entrepreneur has chosen e1 in the former case should lead a bank to give a loan whereas observing e2 in the latter case should lead a bank to not give a loan. We nd that banks in the Bad Framework with reputation give a loan 83% of the time when they meet an entrepreneur who has chosen e1 at least once previously. This is quite close to the predicted 100%. Banks give a loan 50% of the time when they are paired with an entrepreneur that has only chosen e2 in the past. Banks, in the Good Framework with reputation, give loans to entrepreneurs who have previously chosen e2 with 21% probability. This is quite close to the predicted 0%. Entrepreneurs who have only chosen e1 receive a loan 72% of the time. There is no such di erence in conditional loan giving in the treatments without reputation in either framework. Table VI: Conditional Loan Giving w/ Reputation w/o Reputation Bad Framework After e1 83% % After only e2 50% % Good Framework After e2 21% 33 35% After only e1 72% %

19 To account for individual heterogeneity we conduct parametric random e ects Probit estimations. For statistical comparisons we nest the with and without reputation treatments for each framework. Results are given in Tables VII and VIII. Note that we are not trying to nd the best model to t our data. We are interested in observing the e ect of reputation, starting in round 2, controlling for other possible explanations. To pick up reputational e ects, we include the variable e1 (the entrepreneur has chosen at least one e1 in the past) in the Bad Framework. e2 is analogously de ned in the Good Framework. 18 We additionally include two variables that theory is silent about. The rst variable, prev_out (bank did not give a loan in the previous round) aims at accounting for the desire of participants to do something instead of just staying out. The second variable, own_succ, counts the number of times the bank has received a payo of 4 from a previous loan among the six concurrently played sequences. This variable was included to isolate reputation e ects from those stemming from learning through own experience. It also reveals whether banks view their interactions with di erent entrepreneurs as distinct. We include round 6 as a separate variable to measure a potential end e ect. In the estimation for the Good Framework we additionally include distinct variables for rounds 3 through 5. The results of the Probit estimations reveal that banks respond to the reputation of the entrepreneur in the intuitive manner. In the Bad Framework, the probability of giving a loan increases by about 24% when a bank observes that the entrepreneur has previously chosen e1. In the Good Framework, the probability of giving a loan decreases by about 16% when the entrepreneur is observed to have chosen inappropriately (i.e. e2) previously. The reputational e ects are additional to any other e ects that might in uence loan giving. Notice that the variable e2 is signi cant in the Good Framework without reputation. Banks are predicted to decrease their probability to give a loan by 16% after an e2. This is surprising as banks in this treatment cannot 18 In the Bad Framework we do not include a separate e2 (only e2) because it would be negatively correlated with e1 for all rounds greater than 1. For the same reason we do not include a separate e1 in the estimations for the Good Framework. For a detailed description of the variables see the Appendix. 19

20 observe the choices of the entrepreneur. Given that the predicted probability to give a loan in the second round is 66%, the marginal e ect brings the probability to give a loan down to a random choice of 50%. Table VII: Results of Random Effects Probit Estimations (Bad Framework) Coe cients Marginal Coe cients Marginal E ects E ects Constant reputation (0.0991) (0.1327) e re (0.1189) (0.1729) prev_out rprev_out (0.1145) (0.1518) own_succ rown_succ (0.0488) (0.0665) round rround_ (0.1283) (0.1751) -Log likelihood Note: Bootstrapped standard errors in parentheses (1000 replications), indicates signi cance on the 5% level Loan giving in the Bad Framework does not change at the end of a sequence. We do, however, observe an end e ect in the Good Framework, where loan giving declines by about 23% in round 6. With reputation, such an e ect is predicted by theory and was found by Camerer and Weigelt (1988). Without reputation such an e ect is not predicted by theory. However, similar end e ects have been found in other related experiments. For example, Russell Cooper, Douglas V. DeJong and Robert Forsythe (1996) nd that cooperation declines sharply in the last round in one shot Prisoner s Dilemma games with a known nite end point. Besides responding to reputation, banks use some aspects of their own past in their decision to give a loan. Banks, in the treatments without reputation in both frameworks, who have not given a loan in the previous round are more likely to stay out again. Their loan giving drops by about 20

21 17% (14%) in the Bad (Good) Framework. In the Bad Framework this tendency is o set in the treatment with reputation. The marginal e ect of reputation is an increase in loan giving by about 18%. We observe that banks in neither framework take their own experience with other entrepreneurs into account when making their choices. That is, the variable own_succ is never signi cant. This suggests that banks treat each interaction with a di erent entrepreneur as distinct. Table VIII: Results of Random Effects Probit Estimations (Good Framework) Coe cients Marginal Coe cients Marginal E ects E ects Constant reputation (0.1190) (0.1781) e re (0.1198) (0.2150) prev_out rprev_out (0.1133) (0.1777) own_succ rown_succ (0.0575) (0.0901) round rround (0.1407) (0.2177) round rround (0.1468) (0.2255) round rround (0.1576) (0.2470) round rround (0.1847) (0.2973) -Log likelihood Note: We report bootstrapped standard errors in parentheses (1000 replications), indicates signi cance on the 5% level 21

22 C. Entrepreneur Behavior The bad (good) reputation prediction is driven by the friendly (unfriendly) entrepreneur choosing the inappropriate (appropriate) action in earlier rounds. 19 Table IX provides information on the proportion of appropriate and inappropriate choices we nd in either framework. Last round choices and choices when mixing is predicted in the Good Framework are omitted. Table IX: Frequency of (In)Appropriate Choices (Predictions in parentheses) e1 in state N if t < 6 13% and no previous e1 e1 if t < 4 85% w/ Reputation w/o Reputation Bad Framework (Inappropriate Choices) (100%) 0% 1 77 (0%) Good Framework (Appropriate Choices) (100%) 60% (0%) Table IX shows that we nd some support for strategic choices in the treatments with reputation. 20 In the Bad Framework, 13% of the choices of the friendly entrepreneurs are in line with reputation building predictions. 21 In the Good Framework this percentage is much higher. We nd 85% of the 19 It is worth noting that the bad (good) reputation prediction involves the entrepreneur revealing (hiding) her type when she is friendly (unfriendly). These are probably not equivalent behavioral tendencies. In this paper, we choose to focus on the fact that revealing (hiding) hurts (bene ts) the short run player. That is, revealing (hiding) involves choosing inappropriate (appropriate) actions in the Bad (Good) Framework. 20 Note that the predictions for the Bad Framework refer to o equilibrium choices whereas the predictions for the Good Framework refer to equilibrium choices. 21 In the Bad Framework with reputation, all observations of choices of inappropriate projects come from 2 entrepreneurs (out of 12). Both were in di erent sessions. One of the two always chooses the inappropriate project when rst given a chance and the other entrepreneur learns to do so after three sequences. 22

23 choices of unfriendly entrepreneurs in line with theoretical predictions. In both cases, theory predicts 100% strategic choices. These results suggest that the good reputation predictions are better supported than the bad reputation predictions. In the Bad Framework without reputation, as predicted, we do not nd any inappropriate choices. In Good Framework without reputation, we nd, contrary to the predictions, 60% appropriate choices. Hence, behavior is close to the predictions of theory in the Bad Framework without reputation and the Good Framework with reputation. In both these treatments theory predicts appropriate choices for the long run player. Behavior sharply deviates from the predictions of theory in the remaining treatments in which theory predicts inappropriate choices for the long run player. IV. Discussion The two surprising results we nd arise because of the higher than predicted earnings of the long run players in (i) the Bad Framework with reputation and (ii) the Good Framework without reputation. In both of these cases the behavior of the short run and the long run players is sharply at odds with the predictions of theory (see Table V and Table IX). We further investigate these ndings in this section. For ease of exposition, and to better motivate the supplementary experiment we conduct, we begin with the Good Framework. One explanation for the high rates of loan giving in the rst 5 rounds, in the Good Framework without reputation, is that the short run players believe that the unfriendly long run players would often choose the appropriate project (e1) if given a loan. Such beliefs would require the long run players to have some other regarding preferences. Noting that when reputation building is not possible all interactions are one shot, we explore this conjecture by conducting a Dictator like game in which a Dictator has to choose between keeping $5 for herself while the other player, the Receiver, obtains $0, or $4 for herself and $4 for the Receiver. This decision mimics the choice faced by an unfriendly entrepreneur in the Good Framework when she is given a loan. In the one shot experiments, we nd that 82% (14/17) of Dictators choose the $4/$4 split. Moreover, we nd that Receivers expect the Dictators to be other regarding, but less than they actually are: only 59% (10/17) believe that the Dictator would choose the $4/$4 split. 23

24 These results suggest an explanation for the behavior we observe in the spirit of homemade priors used by Camerer and Weigelt (1988). That is, the approximately 60% of short run players who give loans do so because they believe the unfriendly long run players will choose the appropriate project. These short run players must believe that 80% of long run players would choose the appropriate action, given that 50% of the long run players are computerized and always choose the appropriate action. This would lead them to prefer giving a loan since giving a loan with such beliefs yields an expected payo of 0:8 (4) + 0:2 (0) = 3:2 > 3, which is the payo from not giving a loan. As expected by the short run players, long run players respond to loan giving by choosing e1 about 60% of the time in the rst ve rounds. 22 This sustains the level of loan giving we observe in the Good Framework without reputation. Another way of interpreting the results in the Good Framework without reputation is provided by noting that the one shot interaction between a bank and an entrepreneur coincides with a Trust game (Berg et al., 1995) with incomplete information about the Trustee s (long run player s) preferences. The excessive loan giving coincides with trusting behavior on the part of the Trustor. In Trust games, as in our setting, this allows the Trustees to earn much more than theoretically predicted. The interpretation provided above is analogous to the Trustors being trusting because the Trustees are trustworthy su ciently often. 23 Can any explanation in the spirit of homemade priors be used to understand the result of too much loan giving in the Bad Framework with reputation? Recall that, in this treatment, short run players are indi erent between giving a loan and not when all long run players choose the appropriate action. We actually observe that some long run players (13%, Table IX) do choose the inappropriate action. Furthermore, our one shot experiment suggests that short run players believe the long run players will choose the inappropriate action more frequently than they actually do. Such beliefs would result in homemade priors of the short run players which imply more than 13% of the long run players choose inappropriately. Such homemade priors should lead the short run players to not give a loan. 22 See Table waii in web Appendix A. 23 See François Cochard, Phu Nguyen Van and Marc Willinger (2004) for a comparison between one shot and repeated Trust games. 24