Continuity of Equilibria for Two-Person Zero-Sum Games with Noncompact Action Sets and Unbounded Payoffs

2016/09/13 by Eugene A. Feinberg, Pavlo O. Kasyanov, Feinberg, Eugene A. +3 · 1 citation
Mathematics · #91A05 #91A44 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:91A05 #msc:91A44

paper · pdf · doi:10.48550/arxiv.1609.03990

arxiv created 2017/09/12 · arxiv updated 2017/09/14

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.

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• An example showing that A-lower semi-continuity is essential for minimax continuity theorems

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