Neutralized Competition

Abstract

This paper proposes a tractable competing mechanism game where each seller simultaneously posts a trading contract that specifies a menu of dominant strategy incentive compatible (DIC) direct mechanisms conditional on an array of messages sent by buyers, and each seller subsequently chooses a DIC direct mechanism from his menu. The complete set of a seller's profits that are supportable in a (symmetric) equilibrium is the interval between the minmax value of his profit with respect to DIC direct mechanisms and his profit in the joint profit maximization. The set of a seller's equilibrium profits is robust to the possibility of a seller's deviation to any arbitrary mechanism in the standard environment with linear utilities and independent private type. Further, with no limited liability or with no capacity constraints, the set of a seller's equilibrium profits coincides with the set of his feasible (i.e., individually rational and incentive compatible) profits. Given a number of buyers, the number of sellers can be endogenized and is equal to the largest number at which a seller's profit in the joint profit maximization is non-negative: As the number of buyers increases, competition is neutralized because only the monopoly terms of trade prevails in the market, whereas the range of a seller's equilibrium profits shrinks to his reservation profit.