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Imperfect Information in Economic Models. Repeated games with imperfect monitoring

Final Activity Report Summary - IMPERFECT MONITORING (Imperfect Information in Economic Models. Repeated games with imperfect monitoring)

The most important scientific achievement under this fellowship is the one included in the paper 'Community enforcement beyond the prisoner's dilemma'. This paper is joint work with Joyee Deb (from New York University) and is currently on the very final stage of preparation to be submitted for publication.

This paper is enclosed into the literature on repeated anonymous random matching games. More precisely, this literature deals with a model of repeated interaction between the agents in a large community. One benchmark application is to a situation where there are many traders that engage repeatedly on pair-wise transactions with other traders. The main goal of this literature is to understand to what extent cooperative behaviour can arise in such a setting (which is a particular instance of repeated games with imperfect private monitoring).

The state of the art of the subject by the time when this project started can be summarised as follows. If information transmission is minimal (i.e. in each period, each trader only observes the outcome in his current transaction), the seminal papers by Kandori and Ellison in the early nineties establish that cooperation can be achieved in the prisoner's dilemma through what they called community enforcement. So far, there had been no successful attempt to generalise their results beyond the prisoner's dilemma without enriching the flow of information between agents. When extra assumptions are made concerning the information available to the agents as the game unfolds, it is possible to get general folk theorems in this context and a good number of papers have established this for different assumptions on information transmission.

The main result in our paper is to establish that, for a general class of games that includes the prisoner's dilemma as a very special instance, a typically large number of payoffs can be obtained as sequential equilibrium outcomes of the corresponding repeated anonymous random matching games (with no extra assumptions on information transmission). This result generalises the findings of Kandori and Ellison and, more importantly, shows that the natural notion of community enforcement identified in their papers is valid beyond the prisoner's dilemma game.

Community enforcement refers to a general class of strategies with the feature that the players' whose behaviour does not adhere to the 'social norm' is ultimately punished not only by those players who observe this 'anomalous behaviour' but by the entire community. The main difference between the strategies used in our construction and their strategies is that we need to start the game with a phase of trust building, but these strategies preserve the feature that the incentives of the players are controlled through community enforcement.