General Competing Mechanisms with Frictions

This paper studies the class of robust equilibria in a general competing mechanism game for decentralized markets with frictions in which non-deviating sellers punish a deviator with dominant strategy incentive compatible (DIC) direct mechanisms. Given one-dimensional, independent, and private types, the lower bound of a seller's payoff in such equilibria is his minmax value over all DIC direct mechanisms if a seller can deviate to a contract that determines a menu of any complex mechanisms conditional on buyers' messages and he chooses a mechanism he wants from it. In applications, the number of sellers is endogenized given a number of buyers and fixed entry costs. As the number of buyer increases, a unique equilibrium emerges and the equilibrium ratio of buyers to sellers converges to the point where a seller's net profit is zero with the monopoly terms of trade.