Analysis of cooperative behavior when utility is semi-transferable

Abstract

The primary purpose of this study is to analyze both cooperative and nonco- operative games under semitransferable utility. In game theory literature, utility seems so far to have been assumed not to be transferable at all in noncoopera- tive games, while both fully transferable and nontransferable utility are con- sidered in the context of cooperative games. There are, however, an abundance of real life situations, where utility is partially transferable. Here we introduce the notion of semitransferable utility, which encompasses full-transferability and nontransferability as its two extreme special subcases. We explore and exem- plify what changes some well-known equilibrium notions undergo when one allows utility to be only partially transferable. In particular, we relate core allocations in a convex cooperative transferable utility (TU) game to their counterparts in a corresponding strategic context, to show that, for each core allocation of a given TU game, there is a strategic form game, where that allocation survives, while almost all other allocations are eliminated.