Refinement of pure Pareto Nash equilibria in finite multicriteria games using preference relations

Naouel Yousfi-Halimi (), Mohammed Said Radjef () and Hachem Slimani ()
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Naouel Yousfi-Halimi: University of Bejaia
Mohammed Said Radjef: University of Bejaia
Hachem Slimani: University of Bejaia

Annals of Operations Research, 2018, vol. 267, issue 1, No 29, 607-628

Abstract: Abstract In this paper, we consider a noncooperative finite multicriteria two-person game G. We study the problem of refinement of Pareto Nash equilibria of G and we propose an approach based on modeling the preferences of the players by two binary relations. This approach follows three main steps: first, we associate to G another game $$\bar{G}$$ G ¯ defined by the two sets of strategies and two binary relations over the set of the strategy profiles, where each binary relation expresses the preferences of the corresponding player. Second, we define a Noncooperative Equilibrium $$\textit{NCE}$$ NCE for the game $$\bar{G}$$ G ¯ and we prove that every $$\textit{NCE}$$ NCE of $$\bar{G}$$ G ¯ is a Pareto Nash equilibrium of G. Third, we propose a procedure for finding the set of $$\textit{NCE}$$ NCE of $$\bar{G}$$ G ¯ independently of how the binary relations are constructed. Moreover, we give three ways to model the preferences of the players by using scalarization and the outranking methods ELECTRE I and PROMETHEE II. All the steps of the proposed approach are completely illustrated through an accompanying example.

Keywords: Finite multicriteria game; Pareto Nash equilibrium; Refinement; Noncooperative equilibrium; Preference relation; Outranking relation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10479-017-2570-8

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