A Reputation-Based Theory of Spatially-Separated Duopoly Competition and Bargaining

A buyer facing two spatially-separated sellers can negotiate with only one potential seller at a time. However, with some delay, the buyer can move back and forth between the two sellers. The introduction of behavioral types, even with low probabilities, makes the equilibrium of the resulting multilateral bargaining problem essentially unique. The equilibrium has a war of attrition structure. The buyer knows the posted price in each store and chooses a seller to visit first. The maximum length of the negotiation that will take place before the buyer leaves to bargain with the other seller is an increasing function of the distance between the stores and the reputation of the second seller. If the sellers post the same initial price, the buyer will never visit one seller more than once in equilibrium. If instead the posted prices are different, a given seller may be visited twice and the buyer may choose to go first to the store with the higher posted price