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.
Mots-clés : Bi-matrix game, Pareto optimal, uncertainty theory, $$-equilibrium
@article{RO_2020__54_2_393_0,
author = {Achemine, Farida and Merakeb, Abdelkader and Larbani, Moussa and Marthon, Philippe},
title = {$Z$-equilibria in {Bi-matrix} games with uncertain payoffs},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {393--412},
publisher = {EDP-Sciences},
volume = {54},
number = {2},
year = {2020},
doi = {10.1051/ro/2019007},
mrnumber = {4069297},
zbl = {1434.91003},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2019007/}
}
TY - JOUR AU - Achemine, Farida AU - Merakeb, Abdelkader AU - Larbani, Moussa AU - Marthon, Philippe TI - $Z$-equilibria in Bi-matrix games with uncertain payoffs JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2020 SP - 393 EP - 412 VL - 54 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2019007/ DO - 10.1051/ro/2019007 LA - en ID - RO_2020__54_2_393_0 ER -
%0 Journal Article %A Achemine, Farida %A Merakeb, Abdelkader %A Larbani, Moussa %A Marthon, Philippe %T $Z$-equilibria in Bi-matrix games with uncertain payoffs %J RAIRO - Operations Research - Recherche Opérationnelle %D 2020 %P 393-412 %V 54 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2019007/ %R 10.1051/ro/2019007 %G en %F RO_2020__54_2_393_0
Achemine, Farida; Merakeb, Abdelkader; Larbani, Moussa; Marthon, Philippe. $Z$-equilibria in Bi-matrix games with uncertain payoffs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 2, pp. 393-412. doi : 10.1051/ro/2019007. http://www.numdam.org/articles/10.1051/ro/2019007/
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