We introduce a notion of upper semicontinuity, weak upper semicontinuity, and show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. We show that our result generalizes the pure strategy existence theorem of Dasgupta and Maskin [3] and that it is neither implied nor does it imply the existen...

We introduce semicontinuity concepts for functions f with values in the space C(Y ) of closed convex subsets of a finite dimensional normed vector space Y by appropriate notions of upper and lower limits. We characterize the upper semicontinuity of f : X → C(Y ) by the upper semicontinuity of the scalarizations σf( · )(y∗) : X → R by the support function. Furthermore, we compare our semicontinu...

in the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{kim} and textit{lee} [w.k. kim and k.h. lee, generalized fuzzy games and fuzzy equilibria, fuzzy sets and systems, 122 (2001), 293-301] and textit{tarafdar} [e. tarafdar, fixed point theorems i...

4 The Dwork-Robba theorem and the upper semicontinuity of ξ 7→ R(ξ,Σ) 9 4.1 The global growth estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.2 The generalized Dwork-Robba theorem . . . . . . . . . . . . . . . . . . . . . . 10 4.3 Upper semicontinuity of ξ 7→ R(ξ,Σ) . . . . . . . . . . . . . . . . . . . . . . . 13 4.4 Continuity of ξ 7→ R(ξ,Σ) at maximal points (Dwork’s tra...

This paper studies the generalized approximate set-valued equilibrium problems and furnishes some new existence results. The existence results for solutions are derived by using the celebrated KKM theorem and some concepts associated with the semi-continuity of the set-valued mappings such as outer-semicontinuity, inner-semicontinuity, upper-semicontinuity and so forth. The results achieved in ...

We investigate two types of semicontinuity for set-valued maps, Painlevé–Kuratowski semicontinuity and Cesari’s property (Q). It is shown that, in the context of convexvalued maps, the concepts related to Cesari’s property (Q) have better properties than the concepts in the sense of Painlevé–Kuratowski. In particular, we give a characterization of Cesari’s property (Q) by means of upper semicon...