Socially Structured Games and Their Applications

METEOR Working Paper No. RM/03/009

26 Pages Posted: 3 Sep 2003

See all articles by P. Jean-Jacques Herings

P. Jean-Jacques Herings

Tilburg University

Gerard van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics; Tinbergen Institute

Dolf Talman

Tilburg University - Department of Econometrics & Operations Research

Date Written: February 27, 2003

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 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 n-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 n-balanced for any choice of n.

The 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.

Keywords: Non-transferable utility game, Core, Balancedness, Nash program

Suggested Citation

Herings, P. Jean-Jacques and van der Laan, Gerard and Talman, Dolf J. J., Socially Structured Games and Their Applications (February 27, 2003). METEOR Working Paper No. RM/03/009, Available at SSRN: https://ssrn.com/abstract=390401 or http://dx.doi.org/10.2139/ssrn.390401

P. Jean-Jacques Herings (Contact Author)

Tilburg University ( email )

Department of Econometrics and Operations Research
P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4668797 (Phone)
5000 LE (Fax)

HOME PAGE: http://https://sites.google.com/view/jean-jacques-herings/home

Gerard Van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Department of Econometrics and Tinbergen Institute
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Dolf J. J. Talman

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands
+31 13 466 2346 (Phone)

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
80
Abstract Views
893
Rank
551,205
PlumX Metrics