Finding All Nash Equilibria of a Finite Game Using Polynomial Algebra

• DOI: 10.48550/arxiv.math/0612462
• Publication Date: 2006-01-01
• Authors: Ruchira S. Datta
• Keywords: Gambit; Stochastic game

The set of Nash equilibria a finite game is the nonnegative solutions to system polynomial equations. In this survey article we describe how construct certain special games and explain find all complex roots corresponding systems, including equilibria. We then systems for arbitrary generic games, by polyhedral homotopy continuation starting from specially constructed games. use Groebner bases solve these learn geometric information about solution varies with payoff functions. Finally, review Gambit software package game.