Game theoretic analysis of a distribution system with customer market search

Consider a distribution system with one supplier and two retailers. When a stockout occurs at one retailer customers may go to the other retailer. We study a single period model in which the supplier may have infinite or finite capacity. In the latter case, if the total quantity ordered (claimed) by the retailers exceeds the supplier's capacity, an allocation policy is involved to assign the limited capacity to the retailers. We analyze the inventory control decisions for the retailers using a game theoretical approach. The necessary and sufficient conditions are derived for the existence of a unique Nash equilibrium. A computational procedure is also proposed to calculate the Nash equilibrium. In case the Nash equilibrium does not exist, we use the concept of Stackelberg game to develop optimal strategies for both the leader and the follower.