Solution Concept for a Non-Cooperative Game With Fuzzy Parameters

Abstract

In this paper, we study a non cooperative game with payoff functions involving fuzzy parameters. We introduce a concept of solution for this game that we call α-N-S- equilibrium. Our definition is derived from the concept of N-S equilibrium introduced by Zhukovskii for a non cooperative game with payoffs involving unknown parameters in the case of complete ignorance of their behavior. The α-N-S- equilibrium takes into account both the aspect of conflict and the aspect of decision making under uncertainty related to the presence of fuzzy parameters. For the aspect of conflict we adopted the Nash equilibrium, for the aspect of uncertainty we adopted the maximin approach through weak Pareto optimality. Furthermore, we give sufficient conditions for its existence.

Bilevel Decision with Generalized Semi-infinite Optimization for Fuzzy Mappings as Lower Level Problems

“…Decision-making problems usually involve vagueness, ambiguity or imprecision which are due to lack of information concerning the environment (see Kacher and Larbani (2003)). Fuzzy set theory, introduced by Zadeh in 1965, is one of the most effective tools used to handle uncertainty in decision-making problems.…”

“…This kind of problem was initially studied by Bellman and Zadeh in 1970, then many literatures gave a great attention for this field. In recent, Kacher and Larbani (2003) studied a noncooperative game with payoff functions involving fuzzy parameters. This paper will discuss some type of bilevel decision problems with the GSIP as lower-level problems.…”

On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies

“…In the context of games involving n-players, there has been a development that delves into non-cooperative games featuring fuzzy parameters. Notably, in [12], a game is examined wherein payoffs depend on certain parameters expressed as fuzzy numbers. These parameters reflect the influence of nature, and the players possess full information, including knowledge of the membership functions of the fuzzy parameters.…”

Existence of Equilibrium Solution for Multi-Leader–Follower Games with Fuzzy Goals and Parameters

“…Fang et al [27] represented the seller and buyers.goals by fuzzy sets in auctions game and investigated the equilibrium existence and computation. Equilibria existence in matrix games, n-person noncooperative games and Stackelberg games with fuzzy parameters were studied in [28][29][30][31][32] respectively. The equilibrium existence in matrix games and n-person noncooperative games with both fuzzy goals and parameters were considered in [33][34][35][36] respectively.…”