Quantitative Economics: Jul, 2012, Volume 3, Issue 2

Finding all pure-strategy equilibria in games with continuous strategies

Kenneth L. Judd, Philipp Renner, Karl Schmedders

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, Bertrand game, dynamic
games,Markov-perfect equilibria.
JEL classification. C63, C73, L13.

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