Paulo Barelli and Idione Soza, School of Economics Discussion Paper No. 467 June 2012, School of Economics, The University of Queensland. Australia.


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In 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.