Definable and Contractible Contracts

This paper analyzes Bayesian normal form games in which players write contracts that condition their actions on the contracts of 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 provide a complete characterization of the set of allocations supportable as pure-strategy Bayesian equilibria of this contracting game. When information is complete, this characterization provides a folk theorem. In general, the set of supportable allocations is smaller than the set supportable by a centralized mechanism designer.