Finding All Pure-Strategy Equilibria in Static and Dynamic Games with Continuous Strategies
AbstractStatic 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. Our examples show that the all-solution methods can be applied to a wide variety of policy-relevant models.
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Bibliographic InfoPaper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 10-45.
Length: 41 pages
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Polynomial equations; multiple equilibria; static games; dynamic games; Markov-perfect equilibria;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
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