Definable and Contractible Contracts

Abstract. This paper analyzes a normal form game in which actions as well as contracts are contractible. The contracts are required to be representable in a formal language. We prove a folk-theorem for games with complete and incomplete information. This is accomplished by constructing contracts which are definable functions of the Godel code of every other player’s contract. We use this to illustrate the ’meet the competition ’ argument from Industrial Organi-zation and the ’principle of reciprocity ’ from Trade and Public Finance. 1. Self Referential Strategies and Reciprocity in Static Games The idea that players in a game might simultaneously commit themselves to react to their competitors actions is heuristically compelling. The best known expression of this idea is well known in the industrial organization literature (e.g. [8]) as the ’meet the competition ’ clause. A similar idea appears in trade theory as the principle of reciprocity ( [1]). This takes the form of trade agreements like GATT that require countries to match tariff cuts by other countries. Finally, tax treaties sometimes have this flavor- 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.