Bertrand game under a fuzzy environment

Abstract

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 (α 1 , α 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 (α 1 , α 2 )-optimistic equilibrium prices and the profits of the fuzzy Bertrand game.