Finding All Pure-Strategy Equilibria in Games with Continuous Strategies
Kenneth L. Judd
Stanford University - The Hoover Institution on War, Revolution and Peace; Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP); National Bureau of Economic Research (NBER)
University of Zurich - Department of Business Administration (IBW)
Swiss Finance Institute; University of Zurich
November 4, 2010
Swiss Finance Institute Research Paper No. 10-45
Static and dynamic games are important tools for the analysis of strategic interactions among economic agents and have found many applications in economics. In many games equilibria can be described as solutions of polynomial equations. In this paper we describe state-of-the-art techniques for finding all solutions of polynomial systems of equations and illustrate these techniques by computing all equilibria of both static and dynamic games with continuous strategies. We compute the equilibrium manifold for a Bertrand pricing game in which the number of equilibria changes with the market size. Moreover, we apply these techniques to two stochastic dynamic games of industry competition and check for equilibrium uniqueness.
Number of Pages in PDF File: 52
Keywords: Polynomial Equations, Multiple Equilibria, Static Games, Dynamic Games, Markovperfect Equilibria
JEL Classification: C63, C73, L13working papers series
Date posted: November 5, 2010 ; Last revised: February 4, 2012
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