The concept of Z-equilibrium has been introduced by Zhuk-ovskii (Mathematical Methods in Operations Research. Bulgarian Academy of Sciences, Sofia (1985) 103-195) for games in normal form. This concept is always Pareto optimal and individually rational for the players. Moreover, Pareto optimal Nash equilibria are Z-equilibria. We consider a bi-matrix game whose payoffs are uncertain variables. By appropriate ranking criteria of Liu uncertainty theory, we introduce some concepts of equilibrium based on Z-equilibrium for such games. We provide sufficient conditions for the existence of the introduced concepts. Moreover, using mathematical programming, we present a procedure for their computation. A numerical example is provided for illustration.

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RAIRO - Operations Research
School of Mathematics and Statistics

Achemine, F. (Farida), Merakeb, A. (Abdelkader), Larbani, M. (Moussa), & Marthon, P. (Philippe). (2020). Z-equilibria in Bi-matrix games with uncertain payoffs. RAIRO - Operations Research, 54(2), 393–412. doi:10.1051/ro/2019007