Annals of Operations Research

, Volume 137, Issue 1, pp 349–368

A Globally Convergent Algorithm to Compute All Nash Equilibria for n-Person Games

Authors

    • Department of EconomicsMaastricht University
  • Ronald Peeters
    • Department of EconomicsMaastricht University
Article

DOI: 10.1007/s10479-005-2265-4

Cite this article as:
Herings, P.J. & Peeters, R. Ann Oper Res (2005) 137: 349. doi:10.1007/s10479-005-2265-4

Abstract

In this paper we present an algorithm to compute all Nash equilibria for generic finite n-person games in normal form. The algorithm relies on decomposing the game by means of support-sets. For each support-set, the set of totally mixed equilibria of the support-restricted game can be characterized by a system of polynomial equations and inequalities. By finding all the solutions to those systems, all equilibria are found. The algorithm belongs to the class of homotopy-methods and can be easily implemented. Finally, several techniques to speed up computations are proposed.

Keywords

computation of all equilibrianoncooperative game theory
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Copyright information

© Springer Science + Business Media, Inc. 2005