Finding all Nash equilibria of a finite game using polynomial algebra
 Ruchira S. Datta
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Abstract
The set of Nash equilibria of a finite game is the set of nonnegative solutions to a system of polynomial equations. In this survey article, we describe how to construct certain special games and explain how to find all the complex roots of the corresponding polynomial systems, including all the Nash equilibria. We then explain how to find all the complex roots of the polynomial systems for arbitrary generic games, by polyhedral homotopy continuation starting from the solutions to the specially constructed games. We describe the use of Gröbner bases to solve these polynomial systems and to learn geometric information about how the solution set varies with the payoff functions. Finally, we review the use of the Gambit software package to find all Nash equilibria of a finite game.
 Title
 Finding all Nash equilibria of a finite game using polynomial algebra
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Economic Theory
Volume 42, Issue 1 , pp 5596
 Cover Date
 201001
 DOI
 10.1007/s001990090447z
 Print ISSN
 09382259
 Online ISSN
 14320479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Nash equilibrium
 Normal form game
 Algebraic variety
 C72
 Industry Sectors
 Authors

 Ruchira S. Datta ^{(1)}
 Author Affiliations

 1. QB3 Institute, University of California, 324 Stanley Hall, Berkeley, CA, 94720, USA