On Equilibrium in Pure Strategies in Games with Many Players

45 Pages Posted: 22 Jan 2004

See all articles by Myrna H. Wooders

Myrna H. Wooders

Vanderbilt University - College of Arts and Science - Department of Economics

Edward Cartwright

De Montfort University

Date Written: December 2003

Abstract

Motivated by issues of imitation, learning and evolution, we introduce a framework of non-cooperative games, allowing both countable sets of pure actions and player types and player types and demonstrate that for all games with sufficiently many players, every mixed strategy Nash equilibrium can be used to construct a Nash-equilibrium in pure strategies that is "equivalent." Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functions and any other attributes that are not directly relevant to other players). The set of crowding attributes is assumed to be compact; this is not required, however, for taste attributes. We stress that for studying issues such as conformity, the case of a finite set of types and actions, while illuminating, cannot yield completely satisfactory results. Our main theorems are based on a new mathematical result, in the spirit of the Shapley-Folkman Theorem but applicable to a countable (not necessarily finite dimensional) strategy space.

Suggested Citation

Wooders, Myrna H. and Cartwright, Edward, On Equilibrium in Pure Strategies in Games with Many Players (December 2003). FEEM Working Paper No. 122.2003. Available at SSRN: https://ssrn.com/abstract=486842 or http://dx.doi.org/10.2139/ssrn.486842

Myrna H. Wooders (Contact Author)

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

Edward Cartwright

De Montfort University ( email )

The Gateway
Leicester, LE1 9BH
United Kingdom

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