Details:
Title  Finding all Nash equilibria of a finite game using polynomial algebra.  Author(s)  Ruchira S. Datta  Type  Article in Journal  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.  Keywords  Nash equilibrium, Normal form game, Algebraic variety  ISSN  09382259; 14320479/e 
URL 
http://link.springer.com/article/10.1007%2Fs001990090447z 
Language  English  Journal  Econ. Theory  Volume  42  Number  1  Pages  5596  Publisher  Springer, Berlin/Heidelberg  Year  2010  Edition  0  Translation 
No  Refereed 
No 
