Bilateral trading and incomplete information: Price convergence in a small market

We study a model of decentralised bilateral interactions in a small market where one of the sellers has private information about her value. There are two identical buyers and another seller, apart from the informed one, whose valuation is commonly known to be in between the two possible valuations of the informed seller. This represents an attempt to model alternatives to current partners on both sides of the market. We consider an infinite horizon game with simultaneous one-sided offers and simultaneous responses. We show that as the discount factor goes to 1, the outcome of any stationary PBE of the game is unique and prices in all transactions converge to the same value. We then characterise one such PBE of the game. JEL Classification Numbers: C78, D82