Repeated Relationships with Limits on Information Processing

Many important strategic problems are characterized by repeated interactions among agents. There is a large literature in game theory and economics illustrating how considerations of future interactions can provide incentives for cooperation that would not be possible in one-shot interactions. Much of the work in repeated games assumes public monitoring: players observe precisely the same thing at each stage of the game. It is well-understood that even slight deviations from public monitoring increase dramatically the difficulty the problems players face in coordinating their actions. Repeated games with private monitoring incorporate differences in what players observe at each stage. Equilibria in repeated games with private monitoring, however, often seem unrealistic; the equilibrium strategies may be highly complex and very sensitive to the fine details of the stochastic relationship between players’ actions and observations. Furthermore, there is no realistic story about how players might arrive at their equilibrium strategies.  We propose an alternative approach to understanding how people cooperate. Each player is endowed with a mental system that processes information: a mental system consists of a number of psychological states and a transition function between states that depends on observations made. In this world, a strategy is just a function from states to actions.  Our framework has the following desirable properties: (i) players restrict attention to a relatively small set of simple strategies. (ii) the number of strategies that players compare is small enough that players might ultimately learn which perform well. We find that some mental systems allow agents to cooperate under a broad set of parameters, while others are not conducive to cooperation.

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