Domain L-Majorization and Equilibrium Existence in Discontinuous Games
AbstractWe 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 InfoPaper provided by Kyiv School of Economics in its series Discussion Papers with number 31.
Date of creation: Jul 2010
Date of revision: May 2011
Note: Revised and resubmitted to Economic Theory
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Majorized correspondence; Qualitative game; Discontinuous game; Better-reply security; Single deviation property;
Find related papers by JEL classification:
- C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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- 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.
- Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
- 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.
- Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, vol. 48(1), pages 31-45, September.
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