A game-theoretic analysis of a market for long-term relationships

In my thesis, I study social interaction of the following form: each agent of an infinite population plays a certain stage game (for example the prisoner’s dilemma) with some opponent in each period. After observing the partners action choice, each player has the option to quit or to maintain the current relationship. If the latter action is chosen by both agents, they will play the game together in the next period, otherwise they return to a “market” for long-term relationships and will be matched randomly with another opponent. The matching process in the market is global and non-assortative: everybody can be matched together with anybody and own behaviour does not affect the probability of being paired up with an agent who plays a certain strategy. Furthermore, there are no information flows between pairs. In the first chapter, “COOPERATIVE EQUILIBRIA IN REPEATED GAMES WITH ENDOGENOUS MATCHING DECISION”, I extend the standard Folk Theorems of Friedman (1971) and Fudenberg and Maskin (1986) to games of this form: I establish a structural difference between models with finitely and infinitely many agents: While with finitely many players any individually rational average payoff can be reached under certain restrictions, this is not possible with infinitely many agents in games of conflicting interests. Nevertheless, it is possible to establish a Folk Theorem for the latter case. Furthermore, I investigate the structure of supporting strategies and prove their optimality for certain stage games. In the second chapter, “IMMITATING COOPERATION AND THE FORMATION OF LONG-TERM RELATIONSHIPS”, I show that the option to maintain or to quit relationships can enforce cooperation in the prisoner's dilemma between boundedly rational agents in a large population if players imitate successful behavior and sometimes choose to experiment. Opposed to the first paper, agents are myopic and do not have the ability to follow history-dependent strategies. However, they have sometimes access to information about what behavior is on average the most successful one. Cooperative behavior in a homogenous population emerges if both the imitation and experimentation rate are sufficiently small. In a heterogeneous population where agents have certain preferences regarding their partner, the same holds without a restriction on the imitation rate. The results resemble Eshel et al. (AER, 1998), but the assumption of local interaction is substituted by the endogenous formation of relationships. Finally, in the third chapter, “ON THE DYNAMICS IN THE MARKET FOR LONG-TERM RELATIONSIPS” (a joint work with Alexander Gaigl), we consider agents who understand the trade-off in the game above, but have no knowledge about the aggregate play of individuals in the market. Agents learn their current opponent's strategy in finitely many periods. Their subjective believe about the aggregate play in the market is based on past experiences. In a first step, we assume that there are infinitely many agents in the population and impose structure on strategies and updating rules. Analytically, and by simulating the model, we derive conditions under which a significant degree of cooperation can be expected. Then, we extend the model to finite populations and show that the dynamics are similar to the infinite case if there are sufficiently many agents. It strikes that the repeated play of strategies which would not support an equilibrium in the same framework with common knowledge, is a stable outcome in many cases