Game Analysis in a Supply Chain Under Lexicographic Allocation Mechanism with Asymmetric Cost

In this paper, we consider a distribution system with one supplier and two retailers who face a same oligopolistic market. The two retailers have different selling price which decreases with the total quantity of the two retailers allocated and their handling cost, respectively. We derive their optimal ordering strategies under Lexicographic Allocation Mechanism (LAM) where the supplier allocates the quantity to one retailer first and then to the other. We investigate how the two retailers compete for the supplier's limited capacity [inventory] in order to maximize their own profits, and gain Nash Equilibria in different interval about the wholesale price.