A note on the equilibrium existence problem in discontinuous games
AbstractIn this note we prove an equilibrium existence theorem for games with discontinuous pay- offs and convex and compact strategy spaces. It generalizes the classical result of Reny (1999) [Econometrica 67, p. 1029-1056], as well as the recent paper of McLennan, Monteiro, and Tourky (2011) [Econometrica 79, p. 1643-1664]. Our condition is simple and easy to verify. Importantly, an example of a spatial location model shows that our conditions allow for eco- nomically meaningful payoff discontinuities, that are not covered by other conditions in the literature.
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Bibliographic InfoPaper provided by School of Economics, University of Queensland, Australia in its series Discussion Papers Series with number 467.
Date of creation: 2012
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-06-25 (All new papers)
- NEP-GTH-2012-06-25 (Game Theory)
- NEP-MIC-2012-06-25 (Microeconomics)
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- Carmona, Guilherme, 2008.
"An Existence Result for Discontinuous Games,"
FEUNL Working Paper Series
wp530, Universidade Nova de Lisboa, Faculdade de Economia.
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- Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
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- 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.
- Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
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