Optimal Multiunit Exchange Design with Single-Dimensionality (Revised version of CARF-F-279)

Abstract

We investigate allocation problems that generalize auction and bargaining, namely multiunit exchanges, where both a central planner and participants bring homogeneous commodities to sell altogether, and there exist restrictions on feasible allocations. We characterize the optimal mechanism in terms of revenue-maximization under dominant strategy incentive compatibility and ex-post individual rationality. We introduce modified virtual valuation, and show that, irrespective of the restrictions, the optimization can be replaced with the maximization of the sum of modified virtual valuations. We apply this result to an important class of allocation problems for heterogeneous items with single-item demands based on Mussa and Rosen (1978).