In this paper, we present a more simple and independent proof of Reny's theorem (1998), on the existence of a Nash equilibrium in discontinue game, with a better-reply secure game in a Hausdorff topological vector space stronger than Reny's one. We will get the equivalence if the payoff function...

In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional strategy spaces in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibrium correspondence and prove...

In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional strategy spaces in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibrium correspondence and prove...