Will more purchasing options benefit customers?

This paper considers the sale of a seasonal product in the face of strategic customers. At the beginning of the selling season, the retailer announces both the price ph at which the product will be sold during the selling season and the post-season clearance price pe<Ph for unsold items. We analyze two operating regimes: The "no reservation regime" allows a buyer either to purchase the product at price ph when he arrives or to enter a lottery to purchase at price pe if the product remains unsold. The "reservation regime" offers each buyer one extra option than the no reservation regime: reserve the product for purchase at the clearance price pe. If the buyer reserves the product under the reservation regime and if it remains unsold at the end of the selling season, then he is obligated to purchase it at price pe. We consider a situation in which heterogeneous customers with probabilistic valuation arrive in accord with a Poisson process. We characterize the rational purchasing behavior wherein each arriving customer is strategic; each customer takes other customers' purchasing behavior into consideration. By considering the Nash equilibrium of this game, we show that strategic customer behavior can render the customer to be worse off and the retailer to be better off under the reservation regime, despite the fact that this regime offers one extra option (reservation) to a customer. Hence, more purchasing options do not necessarily benefit customers.