We 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...

In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened: roughly, we introduce a measure...

Payoff security combined with reciprocal upper semicontinuity is sufficient for better-reply security, and consequently for the existence of a pure strategy Nash equilibrium in compact, quasiconcave games by Reny's (1999) theorem. Analogously, diagonal payoff security combined with upper...

We provide conditions that simplify applying Reny's (1999) better-reply security to Bayesian games and use these conditions to prove the existence of equilibria for classes of games in which payoff discontinuities arise only at “ties.” These games include a general version of all-pay...

We study whether we can weaken the conditions given in Reny (1999) and still obtain existence of pure strategy Nash equilibria in quasiconcave normal form games, or, at least, existence of pure strategy $\varepsilon-$equilibria for all epsilon0. We show by examples that there are: (1)...

This paper analyzes the traditional unidimensional, two-party electoral competition game when parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. In spite of having discontinuous payoffs, this game,...