Abstract

http://ssrn.com/abstract=1703417
 
 

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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)

Philipp Renner


University of Zurich - Department of Business Administration (IBW)

Karl H. Schmedders


Swiss Finance Institute; University of Zurich

November 4, 2010

Swiss Finance Institute Research Paper No. 10-45

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.

Number of Pages in PDF File: 52

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

JEL Classification: C63, C73, L13

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Date posted: November 5, 2010 ; Last revised: February 4, 2012

Suggested Citation

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

Contact Information

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
University of Zurich - Department of Business Administration (IBW) ( email )
Moussonstrasse 15
Zurich, CH-8044
Switzerland
0041446343782 (Phone)
Karl H. Schmedders (Contact Author)
Swiss Finance Institute ( email )
c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
Switzerland

University of Zurich ( email )
Moussonstrasse 15
Zürich, CH-8044
Switzerland
+41 (0)44 634 3770 (Phone)
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