Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem

We provide a pure Nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of Reny (1999). In comparison with Reny's argument, our proof is brief. Our result subsumes a prior existence result of Nishimura a...

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Bibliographic Details
Published in:Econometrica 2011-09, Vol.79 (5), p.1643-1664
Main Authors: McLennan, Andrew, Monteiro, Paulo K., Tourky, Rabee
Format: Article
Language:English
Subjects:
Applications
better reply security
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
diagnosable games
discontinuous payoffs
Economic models
Economic theory
Equilibrium models
Exact sciences and technology
existence of equilibrium
Existence theorems
Game theory
Games of strategy
Insurance, economics, finance
Mathematical discontinuity
Mathematical functions
Mathematics
multiple restrictional security
Nash equilibrium
Noncooperative games
Pay-off
Probability and statistics
pure Nash equilibrium
Residential segregation
Sciences and techniques of general use
Statistics
Studies
Topological spaces
Topological vector spaces
Working papers
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Summary:We provide a pure Nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of Reny (1999). In comparison with Reny's argument, our proof is brief. Our result subsumes a prior existence result of Nishimura and Friedman (1981) that is not covered by his theorem. We use the main result to prove the existence of pure Nash equilibrium in a class of finite games in which agents' pure strategies are subsets of a given set, and in turn use this to prove the existence of stable configurations for games, similar to those used by Schelling (1971, 1972) to study residential segregation, in which agents choose locations.
ISSN:0012-9682
1468-0262
DOI:10.3982/ECTA8949