Denable 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 de…nable 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. 1 Self Referential Strategies and Reciprocity in Static Games In this paper we characterize the allocation rules attainable by players in a Bayesian game when they have the ability to commit themselves by writing contracts that condition on other players’ contracts. The idea that contracts might condition on other contracts is not new in economics. The most commonly known expression of this idea is well known in the industrial organization literature (e.g. (Salop 1986)) as the ’meet the competition’clause in which one …rm commits itself to lower its price when any of its competitors does. A similar idea appears in trade theory as the principle of reciprocity ((Bagwell and Staiger 2001)). Countries enact trade legislation in which they agree to abide by a trade agreement like GATT. Such legislation commits the country to lowering tari¤s in response to trade legislation by another country that lowers tari¤s, provided this other country’s legislation agrees to abide by GATT. Finally, tax treaties sometimes have this ‡avor for example, out of state residents who work in Pennsylvania are exempt from Pennsylvania tax as long as they live in a state that has a ’reciprocal’agreement that exempts out of state residents (presumably from Pennsylvania) from state taxes.1 We would like to thank the editor and three referees for many useful suggestions that we ended up incorporating into the paper. 1http://www.revenue.state.pa.us/revenue/cwp/view.asp?A=238&Q=244681