A three-person game theory model arising in stochastic inventory control theory

In this paper, we build a game theory model for a single-period inventory problem where each of three retailers tries to determine his optimal order quantity. Their products are substitutable and have random demands. Therefore, multiple direction demand transfers occur when one or more retailers are sold out. It is shown that, by using Nash equilibrium, optimal decision exists for each retailer when they work independently. The optimal order …