Volume 54, Number 2, March-April 2020
|Page(s)||393 - 412|
|Published online||27 February 2020|
Z-equilibria in Bi-matrix games with uncertain payoffs
Université Mouloud Mammeri de Tizi-Ouzou, Algeria
2 L2CSP, Université Mouloud Mammeri de Tizi-Ouzou, Algeria
3 School of Mathematics and statistics, Carleton Unversity, Ottawa, Canada
4 IRIT-ENSEEIHT, Université Fédérale Toulouse Midi-Pyrénées, 31000 Toulouse, France
* Corresponding author: firstname.lastname@example.org
Accepted: 31 December 2018
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.
Mathematics Subject Classification: 91A05 / 90B50 / 68T37
Key words: Bi-matrix game / Pareto optimal / uncertainty theory / Z-equilibrium
© EDP Sciences, ROADEF, SMAI 2020
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