Socially structured games and their applications

Abstract

In this paper we generalize the concept of a non-transferable utility game by introducing the concept of a socially structured game.A socially structured game is given by a set of players, a possibly empty collection of internal organizations on any subset of players, for any internal organization a set of attainable payo.s and a function on the collection of all internal organizations measuring the power of every player within the internal organization.Any socially structured game induces a non-transferable utility game.In the derived nontransferable utility game, all information concerning the dependence of attainable payo.s on the internal organization gets lost.We show this information to be useful for studying non-emptiness and re.nements of the core. For a socially structured game we generalize the concept of p-balancedness to social stability and show that a socially stable game has a non-empty socially stable core.In order to derive this result, we formulate a new intersection theorem that generalizes the KKM-Shapley intersection theorem.The socially stable core is a subset of the core of the game.We give an example of a socially structured game that satis.es social stability, whose induced non-transferable utility game therefore has a non-empty core, but does not satisfy p-balanced for any choice of p.The usefulness of the new concept is illustrated by some applications and examples.In particular we de.ne a socially structured game, whose unique element of the socially stable core corresponds to the Cournot-Nash equilibrium of a Cournot duopoly.This places the paper in the Nash research program, looking for a unifying approach to cooperative and non-cooperative behavior in which each theory helps to justify and clarify the other.