Bertrand game under a fuzzy environment

Players are often assumed to be perfect rational in Bertrand game. However, the decision-making of players is influenced by their behavioral characteristic, psychology preferences and other uncertain factors. Therefore, this paper focuses on investigating the price strategies of players with risk aversion in a Bertrand game under a fuzzy environment. Based on the credibility theory, a fuzzy Bertrand game model with risk aversion is constructed, where optimistic value criterion is applied to model players' risk aversion. The market demand for each player is assumed as a fuzzy variable. Then, a solution concept of the (alpha(1), alpha(2))-optimistic equilibrium price is defined and investigated. Finally, some numerical studies are applied to analyze how the risk aversion behavior of players (the confidence levels of players) affects the (alpha(1), alpha(2))-optimistic equilibrium prices and the profits of the fuzzy Bertrand game.