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

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, al...

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Bibliographic Details
Published in:Annals of operations research 2022-10, Vol.317 (2), p.537-568
Main Authors: Feinberg, Eugene A., Kasyanov, Pavlo O., Zgurovsky, Michael Z.
Format: Article
Language:English
Subjects:
Analysis
Business and Management
Combinatorics
Continuity (mathematics)
Control theory
Cost function
Decision-making
Feinberg: Probability
Game theory
Inventory control
Markov analysis
Markov processes
Mathematical optimization
Minimax technique
Operations research
Operations Research/Decision Theory
Theory of Computation
Zero sum games
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Summary: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.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-017-2677-y