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Domain L-Majorization and Equilibrium Existence in Discontinuous Games


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  • Pavlo Prokopovych

    (Kyiv School of Economics, Kyiv Economic Institute)


We study the equilibrium existence problem in normal form and qualitative games in which it is possible to associate with each nonequilibrium point an open neighborhood and a collection of deviation strategies such that, at any nonequilibrium point of the neighborhood, a player can increase her payoff by switching to the deviation strategy designated for her. An equilibrium existence theorem for compact, quasiconcave games with two players is established. We propose a new form of the better-reply security condition, called the strong single deviation property, that covers games whose set of Nash equilibria is not necessarily closed. We introduce domain L-majorized correspondences and use them to study equilibrium existence in qualitative games.

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Bibliographic Info

Paper provided by Kyiv School of Economics in its series Discussion Papers with number 31.

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Date of creation: Jul 2010
Date of revision: May 2011
Handle: RePEc:kse:dpaper:31

Note: Revised and resubmitted to Economic Theory
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Keywords: Majorized correspondence; Qualitative game; Discontinuous game; Better-reply security; Single deviation property;

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  1. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, Econometric Society, vol. 67(5), pages 1029-1056, September.
  2. Bagh, Adib, 1998. "Equilibrium in abstract economies without the lower semi-continuity of the constraint maps," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 175-185, September.
  3. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, Springer, vol. 48(1), pages 31-45, September.
  4. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, Springer, vol. 48(1), pages 5-16, September.
  5. Luciano I. de Castro, 2008. "Equilibria Existence in Regular Discontinuous Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1463, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 60(4), pages 935-48, October.
  7. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
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