Solutions for zero-sum two-player games with noncompact decision sets and unbounded payoffs

被引：0

作者：

Feinberg, Eugene A. ^{[1
]}

Kasyanov, Pavlo O. ^{[2
]}

Zgurovsky, Michael Z. ^{[2
]}

机构：

[1] SUNY Stony Brook, Dept Appl Math & Stat, Stony Brook, NY 11794 USA

[2] Natl Tech Univ Ukraine, Inst Appl Syst Anal, Igor Sikorsky Kyiv Polytech Inst, Kiev, Ukraine

来源：

NAVAL RESEARCH LOGISTICS | 2023年 / 70卷 / 05期

关键词：

noncompact action sets; solution; two-person game; unbounded payoffs; value; MINIMAX INEQUALITIES; KKM THEOREM; EXISTENCE; EQUILIBRIA;

D O I：

10.1002/nav.22111

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This article provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and we do not assume any convexity/concavity-type conditions. For such games expected payoff may not exist for some pairs of strategies. The results of this article imply several classic facts. The article also provides sufficient conditions for the existence of a value and solutions for each player. The results of this article are illustrated with the number guessing game.

引用

页码：493 / 506

页数：14

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