KKM and Nash Equilibria Type Theorems in Topological Ordered Spaces

Luo, Qun

doi:10.1006/jmaa.2001.7624

Cited by 15 publications

(10 citation statements)

References 5 publications

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“…Finally we get collectively fixed point theorems on abstract convex spaces. In each section, we show that the generalized forms of consequences in [1,2,6,7] on topological semilattices with path-connected intervals follow from our results.…”

Section: Introductionsupporting

confidence: 56%

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Applications of Results on Abstract Convex Spaces to Topological Ordered Spaces

Kim¹

2013

Bulletin of the Korean Mathematical Society

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Abstract. Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..

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Section: Introductionsupporting

confidence: 56%

“…On such semilattices, Luo [6,7] obtained a KKM theorem and Ky Fan's section theorems, and Al-Homidan et al [1] obtained a collectively fixed point theorem for a family of multimaps.…”

Section: Introductionmentioning

confidence: 99%

Applications of Results on Abstract Convex Spaces to Topological Ordered Spaces

Kim¹

2013

Bulletin of the Korean Mathematical Society

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“…But an interest to Nash equilibria in more general frames is rapidly growing in last decades. For instance, Aliprantis, Florenzano and Tourky [1] work in ordered topological vector spaces, Luo [9] in topological semilattices, Vives [17] in complete lattices. Briec and Horvath [2] proved the existence of Nash equilibrium point for B-convexity and Max-Plus convexity.…”

Section: Introductionmentioning

confidence: 99%

Equilibria for games in idempotent measures

Radul

2017

ESAIM: ProcS

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Abstract. This paper is devoted to non-cooperative games in idempotent measures. We consider two kinds of such games. Firstly, players are allowed to play their mixed idempotent strategies. We also consider games where belief of each player about a choice of the strategy by the other players is an idempotent measure. We prove existence of equilibria in both cases and discuss the difference between them.

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“…If Y = R = (−∞, +∞) and C = [0, +∞), and F = ϕ is a real function, then the C-∆-quasiconvexity of ϕ is equivalent to the ∆-quasiconvexity of ϕ (see [10]). Definition 2.6.…”

Section: The Setmentioning

confidence: 99%

“…Since then, KKM theory is continued in topological semilattices with some papers of Luo [10,11], Vinh [17,17,18].…”

Section: Introductionmentioning

confidence: 99%