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Homotopy methods to compute equilibria in game theory

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  • P. Herings

    ()

  • Ronald Peeters

Abstract

This paper presents a complete survey of the use of homotopy methods in game theory.Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by variousselection theories. We present all relevant techniques underlying homotopy algorithms.We give detailed expositions of the Lemke-Howson algorithm and the Van den Elzen-Talman algorithm to compute Nash equilibria in 2-person games, and the Herings-Vanden Elzen, Herings-Peeters, and McKelvey-Palfrey algorithms to compute Nash equilibriain general n-person games.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 42 (2010)
Issue (Month): 1 (January)
Pages: 119-156

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Handle: RePEc:spr:joecth:v:42:y:2010:i:1:p:119-156

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Related research

Keywords: Homotopy; Equilibrium computation; Non-cooperative games; Nash equilibrium; C62; C63; C72; C73;

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References

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Citations

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Cited by:
  1. Ron Borkovsky & Ulrich Doraszelski & Yaroslav Kryukov, 2012. "A dynamic quality ladder model with entry and exit: Exploring the equilibrium correspondence using the homotopy method," Quantitative Marketing and Economics, Springer, vol. 10(2), pages 197-229, June.
  2. Borkovsky, Ron N. & Doraszelski, Ulrich & Kryukov, Yaroslav, 2009. "A Dynamic Quality Ladder Model with Entry and Exit: Exploring the Equilibrium Correspondence Using the Homotopy Method," CEPR Discussion Papers 7560, C.E.P.R. Discussion Papers.
  3. Iryna Topolyan, 2013. "Existence of perfect equilibria: a direct proof," Economic Theory, Springer, vol. 53(3), pages 697-705, August.
  4. Bernhard Stengel, 2010. "Computation of Nash equilibria in finite games: introduction to the symposium," Economic Theory, Springer, vol. 42(1), pages 1-7, January.

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