مقاله سال ۲۰۱۶

 مجله امگا – Omega

Many transactions between a seller and a buyer follow some form of a negotiation. This is typical in business-to-business settings as well as in transactions that involve end consumers for expensive items such as cars, furniture, and real-estate [5,, 16,, 18]. There are also examples in consumer commerce [34,, 19,, 15,7,10,30]. The outcome of each such negotiation depends on the reservation values of the seller and buyer, their negotiation skills, and their beliefs on the same parameters of their opponent. This process is known as a “bilateral negotiation”, and if the focus of the negotiation process is restricted to prices specifically, as “bilateral price negotiations”.

Despite the importance and prevalence of negotiation problems in practice, quantitative dynamic pricing and revenue management, which has “evolved into a mature research area to support a seller’s tactical capacity allocation choices and pricing decisions with inventory considerations [24]” has mostly focused on posted price mechanisms [11,35] and auctions [36]. There have been several extensions of the classical revenue management problem, for instance Bodily and Weatherford [4] consider the situations with continuous resources and several pricing classes; Sen [32] develops dynamic pricing heuristics as an extension to the Gallego and Van Ryzin’s model that perform substantiall\y better than the fixed price policy. Lan et al. [20,21] provide successful examples of combining the overbooking and seat allocation decisions with the regret models. (Among other interesting line of research lie Kim and Bell’s work [17] on the optimal pricing and production decisions in the presence of substitution, Tsai and Hung’s paper [33] on the use of integrated real options internet retailing, Zhao et al. [37] regarding dynamic pricing in the presence of customer inertia, and Ghoniem and Maddah [13] optimizing retail assortment, pricing, and inventory decisions with substitutable products.) However, this broad research area has largely ignored the bilateral price negotiation problems perhaps regarding them as being in the scope of game theory. However, as we emphasize in this paper, the two problem types could be very similar and revenue management methods can be readily applicable in bilateral negotiation problems.

In more detail, we hereby focus on the revenue maximization problem of a vendor that has C units of capacity to sell over a time horizon of length T to a market of prospective buyers. These buyers arrive according to a Poisson process with rate Λ, each has a willingness-to-pay that is an independent draw from a distribution Fb, and engage in a bilateral negotiation with the seller for a single unit. The salvage value of the seller is private information, and buyers assume that it follows some distribution Fs and is constant over time. The reservation price of the seller at time t depends on the salvage value and the state of the sales process, i.e., the time-to-go and remaining capacity. The bilateral negotiation is modeled as a one-off negotiation, where the buyer and seller submit bids and where the unit is awarded if the buyer’s bid is higher than the seller’s bid. When the seller has market power, the transaction price is the seller’s posted price (SPP); when the buyer has market power, the transaction price is the buyer’s posted price (BPP); in other cases the transaction price splits the difference between the two bids according to a fixed ratio that models the relative negotiation power of the two players.1