Inefficiency in a Frictionless Market

Abstract

Gale and Sabourian (2006) discuss the existence of inefficient Markov-perfect equilibrium (MPE) in a heterogeneous market. This paper shows that the example they provide cannot be supported as a MPE. Indeed, with two buyers and two sellers, the dispersion of bargaining positions is not sufficiently wide to support any inefficient trades in their setup. I then prove that their conjecture is correct by constructing a continuum of inefficient MPE with three buyers and three sellers, where the dynamics of continuation payoffs is rich enough to support wide dispersion of bargaining positions at the first stage, which in turn renders inefficient trades individually rational. This suggests that the number of players in a market could be essential for allocative inefficiency.

Keywords: Bargaining, markov-perfect equilibrium, random matching, allocative efficiency, frictionless

JEL Classification: C72, C78, D5