Game-theoretical Models of a Two-echelon Supply Chain Involving Two Substitutable Products

This paper considers tripartite pricing issues in a two-echelon supply chain involving duopolistic manufacturers and a single retailer. Firstly, a tripartite competitive model is conducted, in which both a Stackelberg game and a Bertrand game occur simultaneously. It is shown that the manufacturer who possesses a higher sales quantity gains more profits than the other one. Secondly, a definition of optimal vertical pricing alliance is proposed when cooperation exists between the retailer and some manufacturer. We conduct two-player games when partial cooperation exists among the three participants. It is demonstrated that the total profit of the alliance is higher than the sum profit of the corresponding two participants in the tripartite competition model, and meanwhile the profit of the manufacturer who is not in the alliance suffers a loss. Further, a criterion is given to judge which manufacturer the retailer will choose to cooperate in order to maximize the total increased profits. From the perspective of game theory, we examine the stability of the vertical alliance with considering the dominance of the retailer. Finally, a numerical illustration is designed to examine the judging criteria of which manufacturer is the member of the optimal alliance under different potential market demands.