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A Note on the Equilibrium Existence Problem in Discontinuous Games
Author(s) -
Barelli Paulo,
Meneghel Idione
Publication year - 2013
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta9125
Subject(s) - mathematical economics , simple (philosophy) , regular polygon , stochastic game , classification of discontinuities , mathematics , economics , mathematical optimization , mathematical analysis , geometry , philosophy , epistemology
In this note, we prove an equilibrium existence theorem for games with discontinuous payoffs and convex and compact strategy spaces. It generalizes the classical result of Reny (1999), as well as the recent paper of McLennan, Monteiro, and Tourky (2011). Our conditions are simple and easy to verify. Importantly, examples of spatial location models show that our conditions allow for economically meaningful payoff discontinuities, that are not covered by other conditions in the literature.