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Computing Equilibria of Dynamic Games

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  • Kenneth Judd
  • Sevin Yeltekin

Abstract

We develop a numerical method for computing all pure strategy subgame-perfect equilibrium values of dynamic strategic games with discrete states and actions. We define a monotone mapping that eliminates dominated strategies, and when applied iteratively, delivers an accurate approximation to the true equilibrium payoffs of the underlying game. Our algorithm has three parts. The first provides an outer approximation to equilibrium values, constructed so that any value outside of this approximation is not an equilibrium value. The second provides an inner approximation; any value contained within this approximation is an equilibrium value. Together, the two approximations deliver a practical check of approximation accuracy. The third part of our algorithm delivers sample equilibrium paths. To illustrate our method, we apply it to a dynamic oligopoly competition with endogenous production capacity.
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Suggested Citation

  • Kenneth Judd & Sevin Yeltekin, "undated". "Computing Equilibria of Dynamic Games," GSIA Working Papers 2011-E20, Carnegie Mellon University, Tepper School of Business.
    • Handle: RePEc:cmu:gsiawp:-962041374
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    File URL: https://student-3k.tepper.cmu.edu/gsiadoc/WP/2011-E20.pdf
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    Cited by:

    1. Santiago R. Balseiro & Huseyin Gurkan & Peng Sun, 2019. "Multiagent Mechanism Design Without Money," Operations Research, INFORMS, vol. 67(5), pages 1417-1436, September.
    2. Susanne Goldlücke & Sebastian Kranz, 2018. "Discounted stochastic games with voluntary transfers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 235-263, July.
    3. Schosser, Josef, 2019. "Consistency between principal and agent with differing time horizons: Computing incentives under risk," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1113-1123.

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