Credibilistic Cournot Game with Risk Aversion under a Fuzzy Environment

Abstract

The classic Cournot game ignores the influence of the players’ psychological behavior on the decision and cannot deal with the game problem of fuzzy information. To address such game situations, a credibilistic Cournot game is developed, where the optimistic value criterion derived from credibility theory is used to describe risk-averse behavior of manufacturers and the associated parameters are characterized by fuzzy variables. Then, a concept of the (α1, α2)-optimistic equilibrium quantity is proposed and its uniqueness is shown. Finally, the relevant results of the credibilistic Cournot game are applied to an example to illustrate the availability of our model, and a sensitivity analysis of the relationship between the (α1, α2)-optimistic equilibrium quantity and confidence levels is performed. The results show that manufacturers’ (α1, α2)-optimistic equilibrium quantity is positively related to the risk aversion level of their competitors and negatively to their own risk aversion level.

Keywords

• Cournot game
• risk aversion
• credibility theory
• optimistic value criterion
• (<i>α</i>₁, <i>α</i>₂)-optimistic equilibrium quantity