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 payoffs 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 non-transferable utility game, all information concerning the dependence of attainable payoffs on the internal organization gets lost. We show this information to be useful for studying non-emptiness and refinements of the core.For a socially structured game we generalize the concept of π-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 satisfies social stability, whose induced non-transferable utility game therefore has a non-empty core, but does not satisfy π-balanced for any choice of πThe usefulness of the new concept is illustrated by some applications and examples. In particular we define 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.
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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number
024.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Herings,P. Jean-Jacques & Laan,Gerard,van der & Talman,Dolf, 2001.
"Measuring the Power of Nodes in Digraphs,"
Research Memoranda
007, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
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