Revenue management with minimax regret negotiations

• We model and solve the 1-to-1 bilateral negotiation problem with uncertainty.
• We establish equivalence of dynamic negotiation and revenue management problems.
• We formulate and solve a fluid formulation of dynamic negotiation problems.
• We extend the fluid formulation to cover uncertainty in dynamic settings.

We study the dynamic bilateral price negotiations from the perspective of a monopolist seller. We first study the classical static problem with an added uncertainty feature. Next, we review the dynamic negotiation problem, and propose a simple deterministic “fluid” analog. The main emphasis of the paper is in analyzing the relationship of the dynamic negotiation problem and the classical revenue management problems; and expanding the formulation to the case where both the buyer and seller have limited prior information on their counterparty valuation. Our first result shows that if both the seller and buyer are bidding so as to minimize their maximum regret, then it is optimal for them to bid as if the unknown valuation distributions were uniform. Building on this result and the fluid formulation of the dynamic negotiation problem, we characterize the seller’s minimum acceptable price at any given point in time.