A two-period dynamic game for a substitutable product inventory control problem

We consider the equilibrium strategies for substitutable product inventory control systems with a random demand in a two-period stationary environment between two retailers. This stationary scenario can be viewed as a dynamic game in a duopoly setting. We formulate the single period game and extend it to the two-period dynamic game. We investigate the existence and uniqueness of the feedback Nash equilibrium with two periods to go. We also suggest a threshold inventory level with two periods to go below which the usual substitution effect on the equilibrium may not be observed. We prove the uniqueness of the equilibrium by imposing more structure on the density function of the demand.