A Note on the Equilibrium Existence Problem in Discontinuous Games


  • Paulo Barelli,

    1. Dept. of Economics, University of Rochester, Rochester, NY 14627, U.S.A.; paulo.barelli@rochester.edu
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  • Idione Meneghel

    1. School of Economics, University of Queensland, Brisbane St. Lucia, QLD 4072, Australia; i.soza@uq.edu.au
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    • This note is extracted from our previously circulated Barelli and Soza (2009). We thank Stephen Morris and three anonymous referees for their comments and extensive suggestions. We would like to thank Phil Reny for invaluable advice throughout this project. We also thank Rabeè Tourky for help with the proofs in this revision. We thank Andrew McLennan for helpful guidance regarding the revision. We acknowledge helpful discussions with Guilherme Carmona, John Duggan, Hari Govindan, Pavlo Prokopovych, Maxwell Stinchcombe, Gábor Virág, and Bob Wilson.


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.