Optimal Mechanism Design with Resale Via Bargaining

In this paper, we examine the optimal mechanism design of selling an indivisible object to one regular buyer and one publicly known buyer, where inter-buyer resale cannot be prohibited. The resale market is modeled as a stochastic ultimatum bargaining game between the two buyers. We fully characterize an optimal mechanism under general conditions. Surprisingly, in this optimal mechanism, the seller never allocates the object to the regular buyer regardless of his bargaining power in the resale market. The seller sells only to the publicly known buyer, and reveals no additional information to the resale market. The possibility of resale causes the seller to sometimes hold back the object, which under our setup is never optimal if resale is prohibited. We find that the seller's revenue is increasing in the publicly known buyer's bargaining power in the resale market. When the publicly known buyer has full bargaining power, Myerson's optimal revenue is achieved; when the publicly known buyer has no bargaining power, a conditionally efficient mechanism prevails