Optimal Bayesian equilibrium for n-person credibilistic non-cooperative game with risk aversion

Article type: Research Article

Authors: Tan, Chunqiao^{a; b; *} | Feng, Zhongwei^a | Li, Cunlin^c | Yi, Wentao^a

Affiliations: [a] School of Business, Central South University, Changsha, China | [b] School of Government Audit, Nanjing Audit University, Nanjing, China | [c] School of Management, Beifang University of Nationalities, Yinchuan, China

Correspondence: [*] Corresponding author. Chunqiao Tan. Tel.: +86 73188830594; Fax: +86 73188710006; E-mail: [email protected].

Abstract: In this paper, a n-person credibilistic non-cooperative game with risk aversion is investigated in the fuzzy environment. Firstly, optimistic value criterion is applied to modeling players’ risk aversion. We define a α-optimistic Nash equilibrium for this games. The existence of α-optimistic Nash equilibrium strategies is proposed. Then a Bayesian α-optimistic Nash equilibrium is given by assuming α to be not common knowledge and its existence theorem is also proved. Moreover, we present a sufficient and necessary condition to find the Bayesian α-optimistic Nash equilibrium. Finally, an example is given to illustrate the usefulness of the proposed game.

Keywords: n-person credibilistic game, risk aversion, fuzzy payoff, Bayesian α-optimistic Nash equilibrium, credibility measure

DOI: 10.3233/JIFS-161917

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 2, pp. 741-751, 2017