A Note on the Equilibrium Existence Problem in Discontinuous Games
Paulo Barelli, Idione Meneghel
Econometrica · 2013 · Volume 81 · Issue 2
Abstract
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.
Keywords
Nash equilibrium, discontinuous payoffs, better reply security, location games
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