Nash Equilibrium For Three Retailers In An Inventory Model With A Fixed Demand Rate

In this paper we consider a competitive inventory control model with a fixed demand rate and initial sudden demands. The model is described as follows: There are three retailers which handle the same kind of products. They simultaneously open their stores and begin to sell it. They make their orders only at the beginning of period. Demands for a retailer occur with a fixed rate and the remaining retailers get initial sudden demands. If shortages happen in a store, unsatisfied demands are reallocated to a neighbor store with strong purchasing power. Moving to buy products causes a time lag in our model. In such a situation, each retailer is planning to minimize the sum of costs related with ordering, holding inventory, shortages and sales. The purpose of each retailer is to decide his order quantity minimizing his total cost. By mathematical formulation, we attempt investigating the optimal strategies for three players. We are interested in a Nash equilibrium analysis giving the optimal strategy in a deterministic demand.