An optimization model of three-player payoff based on fuzzy game theory in green supply chain

Abstract

In this paper an optimization fuzzy game model of three-player payoff is developed, that is affected by customer demands in a green supply chain. This model proposes a practical solution to increase the players’ confidence to choose green strategies. At first, the strategies of players: government, manufacturer and customer are formulated by using game theory and then, in order to optimize the player's payoff function in uncertain conditions of customer demand, the model is combined with fuzzy sets theory in related variables and parameters. Finally, a method of problem solving is presented by Nash equilibrium. To speed up calculations and problem solving, a computational fuzzy program is designed with the capability of sensitive analysis by changing the fuzzy variables and parameters. This model is particularly designed for governments and manufacturers to analyze the effect of customer’s decisions on their strategies, related income/cost parameters that results in the optimized strategy selection, and improved payoff. For the evaluation of the model, a numeral analysis is presented to compare the positive effects of this fuzzy game model on players’ payoff function optimization in uncertain conditions against the non-fuzzy game model.