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

P.J.J. Herings*, R.J.A.P. Peeters

*Corresponding author for this work

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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.
Original languageEnglish
Pages (from-to)349-368
JournalAnnals of Operations Research
Volume137
DOIs
Publication statusPublished - 1 Jan 2005

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