Optimal bargaining mechanisms with refusal cost

We consider a bargaining situation between an arriving buyer and a seller, where the buyer and the seller have private valuations. The seller has an inventory, which has to be sold over the infinite horizon. It is assumed that the seller incurs a refusal cost, if the trade does not take place. Myerson (1985) discusses four bilateral bargaining mechanisms in static settings - price negotiation, splitting the difference between seller's and buyer's offer, buyer posted price and seller posted price. The objective of this research is to study these mechanisms in the dynamic setting, with consideration of the refusal cost. In this paper, we model the situation as a Markov decision process, which endogenises the seller's marginal inventory valuation. We find that the seller prefers posting prices when the refusal cost is low. Seller is indifferent between buyer posted price and negotiation for the high refusal cost.