Supplier-Buyer Negotiation Games: Equilibrium Conditions and Supply Chain Efficiency

In a decentralized supply chain, supplier-buyer negotiations have a dynamic aspect that requires both players to consider the impact of their decisions on future decisions made by their counterpart. The interaction generally couples strongly the price decision of the supplier and the quantity decision of the buyer. As a result, the outcome of the negotiation may not have an equilibrium. We propose a basic model for a repeated supplier-buyer interaction, during a number of rounds. In each round, the supplier first quotes a price, and the buyer places an order at that price. We find conditions for existence and uniqueness of subgame-perfect equilibrium in the dynamic game. We furthermore identify some demand distributions for which these conditions are met, when costs are stationary and there are no holding costs. In this scenario and for such demands, we examine the efficiency of the equilibrium and in particular show that, as the number of rounds increases, the profits of the supply chain increase towards the supply chain optimum.