Competitive Revenue Management with Sequential Bargaining

Abstract

When firms post prices to sell their products in a competitive market, buyers often seek to bargain down the prices. The existing studies on dynamic competition, however, focus on firms’ dynamic pricing strategies without considering the possibility of bargaining. We model a random stream of buyers with heterogeneous valuations who may choose to negotiate for a discount from a posted price. When bargaining is allowed, a seller firm's competing strategy depends not only on her reservation value (i.e., her gain from an unsold item when losing the current buyer to the opponent) but also on her disagreement point (i.e., the value of an unsold item when the negotiation with an arriving buyer breaks down). We show that the reservation values and the disagreement points can play opposite roles in competition—the seller firms’ posted prices are increasing in their reservation values but are decreasing in their disagreement points. In general, a seller becomes more aggressive in price competition when her reservation value becomes lower. However, it is not always the case that a seller with a lower reservation value can successfully win the deal from an arriving buyer, as it is in pure price competition. Because of the possibility of bargaining, the buyer may end up purchasing from a seller who has a higher inventory level and a higher reservation value when the seller's disagreement point is lower than that of her opponent. Interestingly, such an equilibrium outcome can only arise when the selling season is sufficiently long. Our analysis highlights the intriguing role played by negotiation in dynamic competition for sequential selling.