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

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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.

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Authors and Affiliations

  1. Department of Economics, Maastricht University, P.O. Box 616, 6200, Maastricht, MD, The Netherlands

    P. Jean-Jacques Herings & Ronald Peeters

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  1. P. Jean-Jacques Herings
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  2. Ronald Peeters
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Correspondence to P. Jean-Jacques Herings.

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Herings, P.JJ., Peeters, R. A Globally Convergent Algorithm to Compute All Nash Equilibria for n-Person Games. Ann Oper Res 137, 349–368 (2005). https://doi.org/10.1007/s10479-005-2265-4

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