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Finding all pure-strategy equilibria in games with continuous strategies


Judd, Kenneth L; Renner, Philipp J; Schmedders, Karl H (2012). Finding all pure-strategy equilibria in games with continuous strategies. Quantitative Economics, 3(2):289-331.

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:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2012
Deposited On:12 Dec 2012 09:55
Last Modified:07 Sep 2017 08:40
Publisher:Wiley-Blackwell
ISSN:1759-7323
Publisher DOI:https://doi.org/10.3982/QE165
Other Identification Number:merlin-id:7325

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