Probabilistic equilibrium solution of soft games

Article type: Research Article

Authors: Deli, Irfan^{a; *} | Çağman, Naim^b

Affiliations: [a] Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, Kilis, Turkey | [b] Department of Mathematics, Faculty of Arts and Sciences, Gaziosmanpaşa University, Tokat, Turkey

Correspondence: [*] Corresponding author. Irfan Deli, Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, 79000 Kilis, Turkey. Tel.: +090348 814 2662; Fax: +090348 814 2663; E-mail: [email protected].

Abstract: In this paper, we give a probabilistic equilibrium solution method of two-person soft games (tps-games). This method can overcome the problem that could not be solved by soft saddle points, soft lower and soft upper values, soft dominated strategies and soft Nash equilibrium. We also prove that every finite tps-game with probabilistic strategies has at least one solution for at least one player. Finally, we give a numerical example which shows that the method can be successfully applied to the game theory.

Keywords: Soft sets, soft games, impact values, probabilistic equilibrium, probabilistic solution methods

DOI: 10.3233/IFS-151992

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 4, pp. 2237-2244, 2016