Finding all pure-strategy equilibria in games with continuous strategies

Kenneth L. Judd*, Philipp Renner, Karl H Schmedders

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)289-331
Number of pages43
JournalQuantitative Economics
Issue number2
StatePublished - Jul 2012


  • Bertrand game
  • Dynamic games
  • Markov-perfect equilibria
  • Multiple equilibria
  • Polynomial equations

ASJC Scopus subject areas

  • Economics and Econometrics


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