Finding All Pure-Strategy Equilibria in Games with Continuous Strategies

Quantitative Economics 3 (2 2012)

Swiss Finance Institute Research Paper No. 10-45

52 Pages Posted: 5 Nov 2010 Last revised: 15 Oct 2014

See all articles by Kenneth L. Judd

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)

Philipp Renner

Lancaster University

Karl Schmedders

University of Zurich

Date Written: November 4, 2010

Abstract

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.

Keywords: Polynomial Equations, Multiple Equilibria, Static Games, Dynamic Games, Markovperfect Equilibria

JEL Classification: C63, C73, L13

Suggested Citation

Judd, Kenneth L. and Renner, Philipp Johannes and Schmedders, Karl, Finding All Pure-Strategy Equilibria in Games with Continuous Strategies (November 4, 2010). Quantitative Economics 3 (2 2012); Swiss Finance Institute Research Paper No. 10-45. Available at SSRN: https://ssrn.com/abstract=1703417 or http://dx.doi.org/10.2139/ssrn.1703417

Kenneth L. Judd

Stanford University - The Hoover Institution on War, Revolution and Peace ( email )

Stanford, CA 94305-6010
United States

Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP) ( email )

5735 S. Ellis Street
Chicago, IL 60637
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Philipp Johannes Renner

Lancaster University ( email )

Managment School
Department of Economics
Lancaster LA1 4YX, Lancashire LA1 4YX
United Kingdom

Karl Schmedders (Contact Author)

University of Zurich ( email )

Moussonstrasse 15
Z├╝rich, CH-8044
Switzerland
+41 (0)44 634 3770 (Phone)

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