Game Theoretic Analysis of a Distribution System in Supply Chain

Abstract

We consider a distribution system in which one supplier provides a single product to several retailers at the beginning of a selling season. The supplier has infinite capacity. The customer demand at each retailer is randomly distributed. Customers who encounter a stockout at one retailer may search other retailers for the product. We study the effects of this market search behavior under both decentralized and centralized control. For the decentralized control model, we show the necessary and sufficient conditions for the existence of a Nash equilibrium, and the sufficient conditions for its uniqueness. For the centralized control model, we find that the payoff function is submodular, and thus we can only obtain allocations that are locally optimal for the entire supply chain. We also design a channel coordination mechanism to match the allocations in the decentralized control model with one of the local optimal allocations under centralized control.