Peters, M.; Szentes, B.; (2009) Definable and contractible contracts. (ELSE Working Papers 327). ESRC Centre for Economic Learning and Social Evolution: London, UK.

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Abstract

This paper analyzes a normal form game in which players write contracts that condition their actions on the contracts of the other players. These contracts are required to be representable in a formal language. This is accomplished by constructing contracts which are definable functions of the Godel code of every other player’s contract. We characterize the set of outcomes that are supportable as (pure strategy) equilibrium with such contracts. With symmetric information, this is all outcomes in which all players receive at least their min max payoff. With incomplete information this all allocation rules that are incentive compatible and satisfy an individual rationality condition that we describe. We contrast the set of allocation rules that can be supported by Bayesian equilibrium with those attainable by a mechanism designer.

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