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Long-Term Relationships as Safeguards ; Can dishonest types induce honest behavior ?

Overview and Results. Recently there has been a surge of interest in how cooperative behavior can arise as an equilibrium outcome in a dynamic community setting. The problem that has to be overcome in such setting is that individuals interact with varying opponents so the usual mechanism of personal and quick retaliation against noncooperators is not available. In this paper we continue this line of research, studying the role of heterogeneity of types, the endogenous formation of long term relationships, and the role of legal institutions in this process. Anecdotal evidence suggests that the endogenous formation of long term relationship may help solve the problem of non-cooperative, or dishonest, behavior. As one example consider the banking industry. The banking literature speaks of “customer relationships,” suggesting that customers who prove themselves to be honest, i.e., who pay back their loans on time, are able to enter into long term relationships and borrow at a lower interest rate or borrow a larger amount. On the other hand, new customers may have to pay a higher interest rate (or borrow a smaller amount) and customers who are not current on their loans are denied credit and may have to turn to other institutions for future business and pay a higher interest rate. Thereby the promise of forming a long term relationship and enjoying higher payoffs and the punishment of severing a relationship, entering into a pool of incognitos, and suffering low payoffs induces borrowers to behave honestly. The model we construct and analyze in this paper delivers these features in a game theoretic setting. More specifically, the setting we consider consists of three elements. The first element is that relationships are constantly reshuffled, i.e., individuals interact with varying opponents over time. This reshuffle is partly exogenous, i.e., induced by exogenously imposed separations and partly endogenous, i.e., induced by individuals’ decisions whether to continue interacting with the same partner or seek a new partner. This implies that the choice of a partner and the longevity of a partnership are, to some extent, endogenous. The second element is that individuals play a prisoner’s dilemma game and are able to observe their partner’s behavior within the relationship (but not his behavior in previous relationships with other agents). Thereby individuals are able to condition their continuation vs. separation decision on that behavior. In particular an individual can leave a partner who cheats her. Conversely, an individual can induce her partner to stay and form a long-term relationship by being honest. The third element of our model is that individual players are of different types. Some players (called good)