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Approximation Results for Discontinuous Games with an Application to Equilibrium Refinement

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  • Oriol Carbonell-Nicolau

    ()
    (Rutgers University)

  • Richard McLean

    ()
    (Rutgers University)

Abstract

We provide approximation results for Nash equilibria in possibly discontinuous games when payoffs and strategy sets are perturbed, and compare these conditions to those considered in the related literature. We then prove existence results for a new "finitistic" infinite-game generalization of Selten's [17] notion of perfection, and study some of its properties. The existence results, which rely on the approximation theorems, relate existing notions of perfection to the new specification.

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Bibliographic Info

Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 201128.

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Length: 20 pages
Date of creation: 16 Aug 2011
Date of revision:
Handle: RePEc:rut:rutres:201128

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Keywords: discontinuous game; Nash equilibrium correspondence; payoff security; trembling-hand perfect equilibrium; limit-of-finite perfect equilibrium;

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References

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  1. Bajoori Elnaz & Flesch János & Vermeulen Dries, 2011. "Perfect equilibrium in games with compact action spaces," Research Memorandum 029, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 569-97, October.
  3. Oriol Carbonell-Nicolau & Richard McLean, 2011. "Approximation Results for Discontinuous Games with an Application to Equilibrium Refinement," Departmental Working Papers 201128, Rutgers University, Department of Economics.
  4. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer, vol. 48(1), pages 17-29, September.
  5. Bagh, Adib, 2010. "Variational convergence: Approximation and existence of equilibria in discontinuous games," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1244-1268, May.
  6. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
  7. Guilherme Carmona, 2011. "Symposium on: Existence of Nash equilibria in discontinuous games," Economic Theory, Springer, vol. 48(1), pages 1-4, September.
  8. Carbonell-Nicolau, Oriol, 2011. "On the existence of pure-strategy perfect equilibrium in discontinuous games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 23-48, January.
  9. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
  10. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
  11. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  12. Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, Open Access Journal, vol. 2(3), pages 235-256, July.
  13. Carbonell-Nicolau, Oriol, 2011. "Perfect and limit admissible perfect equilibria in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 531-540.
  14. Al-Najjar, Nabil, 1995. "Strategically stable equilibria in games with infinitely many pure strategies," Mathematical Social Sciences, Elsevier, vol. 29(2), pages 151-164, April.
  15. Bernard Lebrun, 1996. "Existence of an equilibrium in first price auctions (*)," Economic Theory, Springer, vol. 7(3), pages 421-443.
  16. Luciano Castro, 2011. "Equilibrium existence and approximation of regular discontinuous games," Economic Theory, Springer, vol. 48(1), pages 67-85, September.
  17. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 27-41, January.
  18. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, 09.
  19. Lebrun, Bernard, 1996. "Existence of an Equilibrium in First Price Auctions," Economic Theory, Springer, vol. 7(3), pages 421-43, April.
  20. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, vol. 48(1), pages 31-45, September.
  21. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
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Citations

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Cited by:
  1. Oriol Carbonell-Nicolau & Richard McLean, 2013. "Approximation results for discontinuous games with an application to equilibrium refinement," Economic Theory, Springer, vol. 54(1), pages 1-26, September.
  2. Oriol Carbonell-Nicolau & Richard McLean, 2012. "On Equilibrium Refinement in Supermodular Games," Departmental Working Papers 201207, Rutgers University, Department of Economics.
  3. Carbonell-Nicolau, Oriol, 2011. "Perfect and limit admissible perfect equilibria in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 531-540.

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