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Optimal Combinatorial Mechanism Design

  • Levent Ulku

    ()

    (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))

We consider an optimal mechanism design problem with several heterogeneous objects and interdependent values. We characterize ex post incentives using an appropriate monotonicity condition and reformulate the problem in such a way that the choice of an allocation rule can be separated from the choice of the payment rule. Central to our analysis is the formulation of a regularity condition, which gives a recipe for the optimal mechanism. If the problem is regular, then an optimal mechanism can be obtained by solving a combinatorial allocation problem in which objects are allocated in a way to maximize the sum of "virtual" valuations. We identify conditions that imply regularity for two nonnested environments using the techniques of supermodular optimization.

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Paper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0903.

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Length: 42 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:cie:wpaper:0903
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  1. Nikolai Kukushkin, 2013. "Monotone comparative statics: changes in preferences versus changes in the feasible set," Economic Theory, Springer, vol. 52(3), pages 1039-1060, April.
  2. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
  3. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer, vol. 8(1), pages 77-101.
  4. Lawrence M. Ausubel & Peter Cramton, 1998. "The Optimality of Being Efficient," Papers of Peter Cramton 98wpoe, University of Maryland, Department of Economics - Peter Cramton, revised 18 Jun 1999.
  5. Motty Perry & Philip J. Reny, 2002. "An Efficient Auction," Econometrica, Econometric Society, vol. 70(3), pages 1199-1212, May.
  6. Levin, Jonathan, 1997. "An Optimal Auction for Complements," Games and Economic Behavior, Elsevier, vol. 18(2), pages 176-192, February.
  7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  8. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-19, July.
  9. 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.
  10. Krishna, Vijay, 2003. "Asymmetric English auctions," Journal of Economic Theory, Elsevier, vol. 112(2), pages 261-288, October.
  11. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
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