Doubly Strong Equilibrium

We present a new concept for (generalized) strategic form games, called \emph{doubly strong equilibrium}, and give an existence result when the players have non-ordered and discontinuous preferences. Since a doubly strong equilibrium is a strong equilibrium in the sense of Aumann, we get the existence of strong equilibria in discontinuous games. The result has been obtained by using the \emph{quasi-Ky Fan minimax inequality}. Applications to exchange economies are given. We prove the existence of \emph{doubly strong allocations}, which maximize consumers' preferences on the set of feasible allocations. The doubly strong allocations belong to the core of the economy. When consumers' preferences are selfish, we have that the doubly strong allocations are fair in the sense of Schmeidler and Yaari. So, we get the existence of fair allocations in the setting of non-ordered and discontinuous preferences.

On the existence of maximal elements, fixed points and equilibria of generalized games in a fuzzy environment

We give new sufficient conditions for the existence of fuzzy maximal elements, fuzzy fixed points and equilibria of generalized fuzzy games. In our results, a key role is played by the existence of upper semicontinuous selection maps of set-valued functions, that we obtain for the class of generalized transfer open lower sections maps