Mixed-Strategy Equilibria in the Nash Demand Game

18 Pages Posted: 29 Aug 2005

See all articles by David A. Malueg

David A. Malueg

University of California Riverside

Date Written: August 23, 2005

Abstract

In the Nash Demand Game each of two players announces the share he demands of an amount of money that may be split between them. If the demands can be satisfied, they are; otherwise, neither player receives any money. This game has many pure-strategy Nash equilibria. This note characterizes mixed-strategy Nash equilibria. The condition critical for existence of an equilibrium is that players' sets of possible demands be balanced. Two sets of demands are balanced if each demand in one set can be matched with a demand in the other set such that they sum to one. For Nash's original game, a complete characterization is given of the equilibria in which both players' expected payoffs are strictly positive.

Keywords: Nash Demand Game, Divide-the-Dollar Game, mixed-strategy equilibria

JEL Classification: C72, C78

Suggested Citation

Malueg, David A., Mixed-Strategy Equilibria in the Nash Demand Game (August 23, 2005). Available at SSRN: https://ssrn.com/abstract=788731 or http://dx.doi.org/10.2139/ssrn.788731

David A. Malueg (Contact Author)

University of California Riverside ( email )

Economics Department
3136 Sproul Hall
Riverside, CA 92505
United States
951 827 1494 (Phone)

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