A globally convergent algorithm to compute all Nash equilibria for n-person games

A globally convergent algorithm to compute all Nash equilibria for n-person games

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Article ID: iaor2006308
Country: Netherlands
Volume: 137
Issue: 1
Start Page Number: 349
End Page Number: 368
Publication Date: Jul 2005
Journal: Annals of Operations Research
Authors: ,
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.

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