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For a class of uncertainty abstract economies in fuzzy environment (UASIFEs), we establish for each UASIFE, the existence of fuzzy strong Berge equilibrium by the Kakutani-Fan Glicksberg fixed point theorem. Moreover, we investigate the stability of equilibrium, and prove that most UASIFEs are essential and each UASIFE has at least an essential component by Fort theorem and reduction to absurdity, respectively.

We study generically stable measures in the local, NIP context. We show that in this setting, a measure is generically stable if and only if it admits a natural finite approximation.

In this paper, we obtain an existence theorem of general strong noncooperative equilibrium point of vector-valued games, in which every player maximizes all goals. We also obtain an existence theorem of strong equilibrium point of vector-valued games with single-leader–multi-follower framework by using the upper semicontinuous of parametric strong noncooperative equilibrium point set of the followers. Moreover, we obtain some results on the generic stability of general strong noncooperative equilibrium point vector-valued games.

In this paper, we mainly study a kind of generalized multiobjective multi-leader–follower games in Hausdorff topological spaces. We establish an existence theorem of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader–follower games. As a special case, we also obtain a sufficient condition on the existence theorem of Nash equilibrium for single-leader–multi-follower games. Moreover, we deduce some results on the generic stability of generalized multiobjective multi-leader–follower games by using the method of essential solutions.

In this paper, we first introduce the notion of cooperative equilibria in multi-leader-multi-follower games, and then establish an existence theorem. Next, we shift out attention to the generic stability of these cooperative equilibria. After studying the class of games satisfying the sufficient conditions of the existence theorem, we identify a dense residual subset of these games whose cooperative equilibria are all essential.

We define the Shapley allocation function (SAF) based on the characteristic function on a set of strategy profiles composed of infinite strategies to establish an n -person biform game model. It is the extension of biform games with finite strategies and scalar strategies. We prove the existence of Nash equilibria for this biform game with SAF, provided that the characteristic function satisfies the linear and semicontinuous conditions. We investigate the essential stability of Nash equilibria for biform games when characteristic functions are perturbed. We identify a residual dense subclass of the biform games whose Nash equilibria are all essential and deduce the existence of essential components of the Nash equilibrium set by proving the connectivity of its minimal essential set.

In this paper, we consider the generic stability of the weakly efficient solution mapping for set-valued optimization problems. Firstly, we obtain the upper semicontinuity of the weakly efficient solution mapping for set-valued optimization problems. Secondly, we show that, in the sense of Baire category, most set-valued optimization problems are stable. Finally, we give sufficient conditions ensuring the existence of essential. Our results extend and improve the corresponding results of Song et al. (J. Optim. Theory Appl. 156:591-599, 2013).

We propose the definition of T -KKM points and consider generic stability of T -KKM mappings and essential components of sets of T -KKM points. As applications, using a unified approach, we derive from these results the existence of essential components of solution sets to various optimization-related problems. We do this in two steps. First, we deduce the corresponding results for variational inclusions, which are new. Then we obtain, as consequences, the existence of essential components of solutions to other problems, which are new or include recent ones in the literature.

In this paper, we introduce a mixed general type of variational relation problems, and establish the existence theorem of solutions of mixed general types of variational relation problems. Moreover, we study the stability of a solution set of mixed general types of variational relation problems. We prove that most of mixed general types of variational relation problems (in the sense of Baire category) are essential and, for any mixed general type of variational relation problems, there exists at least one essential connected component of its solution set. MSC: 49J53, 49J40.

In this paper, we study minimax regret equilibria. First, existence theorem of minimax regret equilibria is proved. Further, the generic stability of minimax regret equilibria is studied. We show that the set of minimax regret equilibria for most of problems (in sense of Baire category) is a singleton set.