Uniform payoff security and Nash equilibrium in compact games

We introduce a condition, uniform payoff security, for games with compact Hausdorff strategy spaces and payoffs bounded and measurable in players’ strategies. We show that if any such compact game G is uniformly payoff secure, then its mixed extension is payoff secure. We also establish that if a uniformly payoff secure compact game G has a mixed extension with reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of compact games satisfying uniform payoff security.