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Optimal Multiunit Exchange Design with Single-Dimensionality


  • Hitoshi Matsushima

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


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).

Suggested Citation

  • Hitoshi Matsushima, 2012. "Optimal Multiunit Exchange Design with Single-Dimensionality," CARF F-Series CARF-F-292, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2012.
  • Handle: RePEc:cfi:fseres:cf292

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    References listed on IDEAS

    1. Susan Athey & Glenn Ellison, 2011. "Position Auctions with Consumer Search," The Quarterly Journal of Economics, Oxford University Press, vol. 126(3), pages 1213-1270.
    2. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 77-101.
    3. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, May.
    4. 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.
    5. Alex Gershkov & Benny Moldovanu, 2009. "Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 168-198, August.
    6. Levent Ülkü, 2013. "Optimal combinatorial mechanism design," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 473-498, June.
    7. 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.
    8. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    9. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    10. Varian, Hal R., 2007. "Position auctions," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1163-1178, December.
    11. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
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    Cited by:

    1. Hitoshi Matsushima, 2015. "Optimal Mechanism Design: Type-Independent Preference Orderings," CIRJE F-Series CIRJE-F-955, CIRJE, Faculty of Economics, University of Tokyo.

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