a: Fractions of strategy types in the buyer population for 200 generations 

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... = - 1 ). If the trust shown by the buyer has been honored by the seller, the seller receives a positive rating ( b = 1 ). Note that the buyer is never rated by the seller and a seller to whom trust was refused is not rated either. A generation consists of a specified number of rounds. In every round an agent interacts with a randomly assigned opponent. Given those parameters, it is improbable that the same buyer-seller pair will occur twice in a generation. Repeated interactions between the same two agents are therefore not accounted for. In every interaction, the buyers decide on the basis of an individually defined strategy whether to trust the sellers or not. In every transaction that takes place as a result of the trust shown by the buyers, the sellers decide on the basis of their own individually defined strategies whether to honor the buyer’s trust or not. Sellers only know their own interaction history. Thus sellers do not know how often a buyer showed no trust. They do, however, know something about the mistrust of buyers in general, since they know how often they were exposed to it themselves. Buyers know their own interaction history and the whole transaction history of the sellers with whom they interacted within the same generation. Explicitly, the buyers know the number of negative ( u ) and positive ( v ) ratings a seller has received, as well as his reputation index r . The reputation index r is calculated from his positive ratings as a fraction of the total number of his transactions ( r = v / (u + v) ). A seller who has not yet engaged in a transaction has no ratings and, as a consequence, a reputation index of r = 0 . The buyer population and the seller population each consist of m = 256 agents. In every generation, every seller and every buyer is involved in k interactions (the length of a generation is therefore k rounds). In order to avoid end-round effects, the generation length is not known before the simulation is executed. At the beginning of the first generation, the buyer strategies are distributed in equal proportions throughout the buyer population; the same applies to the distribution of seller strategies in the seller population. At the end of every generation, the payoffs that all agents with the same strategy have obtained are summed into a total score. Then, in the next generation the strategies are distributed throughout the population of buyer and seller agents respectively, in proportion to the scores they have obtained. Neither history, ratings nor the reputation of a parent agent are transferred to a child agent in the next generation. First, we conduct simple scenario experiments in which we test different ad-hoc buyer and seller strategies. Therewith, we explore the effects on the level of trust and cooperation in the system the properties of the employed strategies and the combination of those have. Second, we arrange tournaments and ask participants to submit their own strategies to compete against other strategies. The tournament approach allows us both to make use of “distributed natural intelligence” in deriving challenges to the mechanisms of our artificial market and to check our experimental findings. 1 In the first scenario experiment we start with a buyer population, half of which consists of agents who always give trust to a seller (ALL C). The other half is composed of agents who never give trust to a seller (ALL D) (see Figure 2a). The seller population in turn is dominated by agents that always honor trust. However, one percent of the seller population consists of agents that never honor trust given by a buyer (see Figure 2b). Although the initial fraction of untrustworthy sellers is very small, these sellers manage to invade the population of trustworthy sellers after 15 generations. At first, the seller population is trustworthy at a very high rate. Agents playing ALL D in the buyer population die out quite early because giving trust is a more successful strategy. After the distrustful buyers have died out, the abuse of trust starts to spread over the seller population. Figure 2c shows that in the beginning, trust is honored at a very high rate, but disappears from the market after the mistrustful buyers’ interactions in which no trust is given. What is left is a market of exploiting sellers and exploitable buyers. In order to protect trustful buyers from exploitation, we introduce a rating mechanism and a buyer strategy which accounts for a seller’s reputation. The initial seller population in scenario 2 consists one half each of trustful and deceitful sellers (see Figure 3b). The buyer population contains, besides the two unconditional strategies ALL C and ALL D, the strategy RT 25. Strategy RT 25 only gives trust to a seller whose reputation index is greater than or equal to r = 0.25 . 2 The initial fraction of both unconditional strategies is 46% of the buyer population. Accordingly, RT 25 starts at a fraction of 8% of the buyer population (see Figure 3a). From the beginning, buyers playing RT 25 discriminate against sellers who do not have a positive reputation. This causes a decrease of the fraction of sellers playing ALL D on the one hand and an increasing fraction of buyers playing RT 25 on the other hand. The strategy RT 25 is more successful than ALL C because it does not get exploited by deceitful sellers. As soon as there are enough trustful sellers and a low rate of sellers playing ALL D respectively, buyers playing ALL C become more successful. Because of their unconditional cooperation, buyers playing ALL C also give trust to sellers without a reputation whereas buyers playing RT 25 do not cooperate with sellers who have not yet established a positive reputation. With the rising success of buyers playing ALL C, sellers playing ALL D have more opportunities to abuse trust and in turn become more successful themselves. At the peak of the deceitful sellers’ success, again, the fraction of buyers playing RT 25 increases while the fraction of buyers playing ALL C decreases. This coevolutionary dynamics is well mapped by the transaction frequencies depicted in Figure 3c. In terms of the interdependence between the abuse of trust, reputation, mistrust, and trust, the dynamics can be described as follows. Starting with a growing rate of abused trust, the reputation mechanism ensures untrustworthy sellers to be recognized and discriminated against. A rising rate of mistrust due to the distrustful buyers’ preference of sellers with a positive reputation is followed by a more confident buyer population and a higher rate of honored trust. The approximate averages of transaction frequencies level off at 60% for Honored Trust, 25% for Mistrust and 15% for Abused Trust. However, if the initial fraction of agents playing RT 25 is below 7%, buyers playing ALL C die out too early, depriving trustworthy sellers of the possibility to build a good reputation. Without a reputation, the strategy RT 25 is not able to distinguish between trustworthy and deceitful sellers and therefore would never give trust in any interaction. Without trustful buyers no transactions take place and without transactions a market does not persist. The results from scenario 2 suggest that trustworthy sellers must get the opportunity to build a positive reputation. Otherwise, conditional strategies like RT 25 would not be able to distinguish between trustworthy and deceitful sellers. A buyer strategy which incorporates that ability and, at the same time, gives sellers without a reputation the opportunity to prove their trustworthiness, is independent of the existence of a more trustful strategy like ALL C. In this scenario, we introduce the strategy RT 25 C. The only difference between RT 25 and RT 25 C is that RT 25 C unconditionally cooperates in its first interaction. Additionally, the initial fraction of buyer agents playing RT 25 C is 6%. Note that at this initial level, the strategy RT 25 failed to establish and maintain a system based on trust and cooperation. Figures 4a, b, and c show the effect of the slight change in buyer strategies. Indeed, the fraction of buyers playing ALL C decreases and the strategy RT 25 C is more successful in this regard. However, it is not self- evident that the success of RT 25 C implies a higher rate of trust and cooperation. RT 25 C, with its single unconditional cooperation is not contingent on confiding buyers playing ALL C and, at the same time, is more successful because not exploitable. Since ALL C fails to survive in the buyer population, the deceitful seller strategy ALL D is not able to persist either. What is left, is a functioning market with trustful but cautious buyers and trustworthy sellers. The scenario experiments show that, despite the lack of an external sanctioning authority, cooperation evolves under two conditions. On the one hand, a minimal fraction of buyers must make use of the sellers’ reputation in their buying strategies. On the other hand, trustworthy sellers must be given opportunities to gain a good reputation through their cooperative behavior. Strategies which account for both these requirements turn out to be successful and conducive to a market based on trust and cooperation at the same time. By organizing round-robin tournaments, we aim to find new seller and buyer strategies that in competing with each other challenge our artificial market system. Strategies were collected at four different occasions and were mostly handed in by students or graduates from different universities and faculties. In every tournament, the best buyer and seller strategy could win a book token that amounted to 20 Euros. The rules to the tournament were told in writing and contained virtually the same information as the section describing the simulation experiments. Figures 5a, b, and c, show a typical run of a tournament with 11 buyer and 22 seller strategies – all strategies that have been handed in so far. KELLER, the winning ...