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Finding All Pure-Strategy Equilibria in Static and Dynamic Games with Continuous Strategies

  • Kenneth L. JUDD

    (Stanford University)

  • Philipp RENNER

    (University of Zurich)

  • Karl SCHMEDDERS

    (Unviersity of Zurich and Swiss Finance Institute)

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. Our examples show that the all-solution methods can be applied to a wide variety of policy-relevant models.

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File URL: http://ssrn.com/abstract=1703417
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Paper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 10-45.

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Length: 41 pages
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Handle: RePEc:chf:rpseri:rp1045
Contact details of provider: Web page: http://www.SwissFinanceInstitute.ch

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