Partner heterogeneity drives strategic reputation building for deception Eva van den Broek and Arthur Schram CREED (Center for Research in Experimental Economics and political Decision-making) Department of Economics and Econometrics, University of Amsterdam II. Heterogeneous (asymmetric info) Aims of the study IV. resultsIII. results By means of a simulation we find that introducing partner variability can undermine the prevailing models of indirect reciprocity. We show that if some interactions are more tempting, the low-payoff interactions are used for building up an image score. The cheater strategy, when confronted with a mixed population of image- scoring fish, performs better than the unconditional defector over a large range of parameters. The speed of convergence of the fish is crucial for the outcome; the interplay between the threshold of the fish and the cleaner strategy makes it hard to analyse the model mathematically. Everyday human social interaction is characterized by asymmetric relations – consider principal-agent relations, owners and intruders, or the biological example of cleaner and client fish. Our simulation model explores the effects of heterogeneity in partner quality on the stability of image scoring (Nowak and Sigmund, 1998). In order to capture both the heterogeneity among partners and the asymmetry in strategy sets, we construct a co-evolutionary model that draws inspiration from cleaner fish interactions with non-predatory clients. The stationary cleaner fish remove parasites from their client’s mouth, but occasionally cheat on living tissue. This threat is counterbalanced by the mobility of the client fish, which can unilaterally end the interaction and switch to another partner. This outside-option controls the level of exploitation by the cleaner fish (Johnstone and Bshary, 2002). It has been shown that the fish form an image score of the cleaners (Bshary, 2002). We extend the population to two different types of client fish, one of them having a higher temptation payoff. Cleaners can condition their strategy on the fish type. What will happen to the image scoring? Conclusion I.Homogeneous (complete info) C D cleaners fish ΘhΘh ΘlΘl flee 6,6 9,12,1 0,2 1,60,2 All fish approach one cleaner and see his image score. If cleaner cooperated last round, image score = 1; otherwise image score = 0. If cleaner’s image score < fish’s threshold level, the fish flees. The classical economic context with asymmetric knowledge about the differences in quality of a product would be Akerlof’s lemon market. However, since the buyer in our model is not aware of how profitable he is to the seller, the situation bears more similarity to an insurance company with a claim bank. The buyer cannot assess his relative risk, and thereby his profitability. Would the company decide to profit heavily from a low-risk (high revenue) client, after having build up a trustworthy image with the high-risk (low revenue) ones? Empirical studies have confirmed that humans use strategic considerations when deciding to help others (see f.i. Semmann, Krambeck, and Milinski, 2004). To establish the effect of individual differences in temptation payoffs on the stability of indirect reciprocity via image scoring, experimental tests are needed. After 10 rounds, offspring is generated based on payoffs. Fish converge to the ‘picky’ threshold 1; cleaners converge to the strategy “cooperate”. All other parameters are the same Threshold of fish drops after initial rise; Cleaners all converge to strategy “cheater”. Coop Def cleaners fish ΘmΘm flee 9/4,6 15/4,1 0,2 Now ¼ of the fish are of type Θ h and ¾ are of type Θ l. Fish only see the image score of the cleaner, own type is unknown to them; Cleaners condition their strategy on the fish type, giving rise to four strategies Θm Θm Θm Θm C D C 101 Average of 30 runs; plotted are the proportions of the two strategies against the number of generations, together with the average threshold of the fish. Θh Θh C AC CH D C Always Coop Always Def ΘhΘh C D ΘlΘl Cheater Rev.Cheater D C C D 1 10 Θl Θl AllC AllD Cheater Fish threshold rCH fish cleaners 0100 generations D Fish threshold generations C Average over 30 runs; plotted are proportions of the four strategies against the number of generations, together with the average threshold of the fish. Cleaners Image scores Fish + type Actions Discussion