Finding All Nash Equilibria of a Finite Game Using Polynomial Algebra

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dc.creatorDatta, Ruchira S.
dc.date2006-12-16
dc.date.accessioned2026-07-07T07:35:28Z
dc.date.available2026-07-07T07:35:28Z
dc.descriptionThe 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 Groebner 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.
dc.descriptionInvited contribution to Journal of Economic Theory; includes color figures
dc.identifierhttps://arxiv.org/abs/math/0612462
dc.identifierhttp://arxiv.org/abs/math/0612462
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120102
dc.subjectCommutative Algebra
dc.subject13P99, 91A10
dc.titleFinding All Nash Equilibria of a Finite Game Using Polynomial Algebra
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