Uniform payoff security and Nash equilibrium in metric games
AbstractWe introduce a condition, uniform payoff security, for games with separable metric strategy spaces and payoffs bounded and measurable in players' strategies. We show that if any such metric game G is uniformly payoff secure, then its mixed extension G is payoff secure. We also establish that if a uniformly payoff secure metric game G has compact strategy spaces, and if its mixed extension G has reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of metric games satisfying uniform payoff security.
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Length: 13 pages
Date of creation: Dec 2005
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Uniform payoff security; Nash equilibrium; discontinuous games; mixed extension.;
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- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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