Continuity of equilibria for two-person zero-sum games with noncompact action sets and unbounded payoffs

Eugene A. Feinberg (), Pavlo O. Kasyanov () and Michael Z. Zgurovsky ()
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Eugene A. Feinberg: Stony Brook University
Pavlo O. Kasyanov: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
Michael Z. Zgurovsky: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

Annals of Operations Research, 2022, vol. 317, issue 2, No 10, 537-568

Abstract: Abstract This paper extends Berge’s maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-player zero-sum games with possibly noncompact action sets and unbounded payoffs. For games with perfect information, also known under the name of turn-based games, this paper establishes continuity properties of value functions and solution multifunctions. For games with simultaneous moves, it provides results on the existence of lopsided values (the values in the asymmetric form) and solutions. This paper also establishes continuity properties of the lopsided values and solution multifunctions.

Keywords: Two-person game; Set-valued mapping; Continuity of minimax; 91A05; 91A44 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-017-2677-y

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