NASH AND STRONGLY CONSISTENT 2-PLAYER GAME FORMS

A two-player game form is Nash-consistent if and only if it is tight ( Gurvich). Therefore Nash-consistency of two-player game forms depends only on the effectivity structure. This fact is no longer true for str ong consistency. In this paper we introduce a new object called the jo int effectivity structure and define the exact joint effectivity set. These notions are similar though more sophisticated than the usual eff ectivity functions. We prove that a two-player game form is strongly c onsistent if and only if it is tight and jointly exact. Joint exactnes s is a property of the exact joint effectivity set which basically req uires that the joint exact effectivity set coincides with the classica l effectivity function. As a corollary we have a characterization of t wo-player strongly implementable social choice correspondences.