Decentralised Bilateral Trading in a Market with Incomplete Information

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, whose valuation is commonly known to be in between the two possible valuations of the informed seller. We consider two in?nite horizon games, with public and private simultaneous one-sided o¤ers respectively and simultaneous responses. We show that there is a stationary perfect Bayes?equilibrium for both models such that prices in all transactions converge to the same value as the discount factor goes to 1.