We consider a multi-period price competition among multiple firms with limited inventories of substitutable products, and study two types of equilibrium: with and without recourse. Under a linear demand model, we show that an equilibrium without recourse uniquely exists. In contrast, we show an equilibrium with recourse need not exist, nor be unique. In a low-influence regime, using the equilibrium without recourse, we construct an approximate equilibrium with recourse with the same equilibrium price trajectory.
