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. In addition to this informed seller, 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 an infinite horizon game with simultaneous one-sided offers and simultaneous responses. We characterise one PBE of the game and show that, as the discount factor goes to 1, prices in all transactions converge to the same value. We then show that this is the case with any stationary equilibrium of the game. That is, the asymptotic outcome is unique across all stationary equilibria.
The authors wish to thank Siddhartha Bandyopadhyay, Martin Cripps, Bhaskar Dutta, Faruk Gul, Ed Green, Vijay Krishna, Sel¸cuk Ozyurt, Larry Samuelson, Asher Wolinsky and Ben Zissimos for their insightful comments and suggestions. We also thank the conference participants of the Royal Economic Society, World Congress of the Econometric Society and the seminar participants at the University of Brown and the Indian Statistical Institute for helpful comments. We sincerely thank the advisory editor and anonymous referees whose helpful comments have made the exposition of this paper much better. We thank the Human Capital Foundation (www.hcfoundation.ru), and especially Andrey P. Vavilov, for support to The Pennsylvania State University’s Department of Economics. Dr Chatterjee would also like to thank the Institute for Advanced Study, Princeton, and the Richard B. Fisher endowment for financial support of his membership of the Institute during the year 2014-15.