Shapley value and other allocation schemes for three-person supply chain games

A game theoretical approach to modelling different supply chains has become a very active area of research in supply chain management during the last two decades. The models that are currently used employed both a non-cooperative and a cooperative approach. Most studies also concentrate on upstream members of the supply chain and ignore the contribution of the consumer downstream and her influence on decisions made by the other members of the chain. In this paper, the consumer, whose purchasing decision would affect the strategies adopted by other players, is an active member of the three-person supply chain games. We present several supply chain models involving a supplier, a retailer and a consumer under both a non-cooperative and cooperative game scenario. Nash equilibrium solutions will be obtained for players in the non-cooperative game, and Pareto and Shapley values in the cooperative game. Numerical examples illustrating and comparing between the different models are also provided.