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Finding all pure-strategy equilibria in games with continuous strategies


Judd, Kenneth; Renner, Philipp; Schmedders, Karl (2011). Finding all pure-strategy equilibria in games with continuous strategies. Swiss Finance Institute Research Paper 10-45, Swiss Finance Institute.

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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2011
Deposited On:15 Feb 2012 08:36
Last Modified:12 Aug 2017 15:34
Series Name:Swiss Finance Institute Research Paper
Number of Pages:49
Additional Information:Presented at ICE Workshop 2011, Chicago
Official URL:http://ssrn.com/abstract=1703417
Other Identification Number:merlin-id:6366

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