Competitive Stock-Replenishment Policies in a Two-Stage Supply Chain

We investigate stock-replenishment problem in a one-warehouse-n-retailer supply chain, in which warehouse supplies single product to n-retailers. When supply chain is designed to gain optimal system cost, some firms intend to deviate the agreement to maximize their profit, and such kind of deviation may cause supply chain inefficiency. In this paper, game theory is used as a tool to balance profit among retailers. When retailers replenish their stock in a Nash Equilibrium, each can maximize own profit while pondering other retailers. Mathematical model for this n-retailer game is constructed. And at last, we prove that there exists at least one equilibrium in this game.