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Optimal Multiunit Exchange Design with Single-Dimensionality

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  • Hitoshi Matsushima

    (Graduate School of Economics, The University of Tokyo, Tokyo)

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).

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Bibliographic Info

Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-292.

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Length: 25 pages
Date of creation: May 2012
Date of revision: Sep 2012
Handle: RePEc:cfi:fseres:cf292

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  1. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
  2. Alex Gershkov & Jacob Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2012. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Working Papers tecipa-445, University of Toronto, Department of Economics.
  3. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, November.
  4. Susan Athey & Glenn Ellison, 2009. "Position Auctions with Consumer Search," NBER Working Papers 15253, National Bureau of Economic Research, Inc.
  5. Monteiro, Paulo Klinger, 2002. "Optimal auctions in a general model of identical goods," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 71-79, February.
  6. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
  7. Levent Ulku, 2009. "Optimal Combinatorial Mechanism Design," Working Papers 0903, Centro de Investigacion Economica, ITAM.
  8. Hitoshi Matsushima, 2011. "Efficient Combinatorial Exchanges with Opt-Out Types," CARF F-Series CARF-F-294, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2012.
  9. Varian, Hal R., 2007. "Position auctions," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1163-1178, December.
  10. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer, vol. 8(1), pages 77-101.
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