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An Assignment Problem with Interdependent Valuations and Externalities

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  • Tatiana Daddario
  • Richard P. McLean
  • Andrew Postlewaite

Abstract

In this paper, we take a mechanism design approach to optimal assignment problems with asymmetrically informed buyers. In addition, the surplus generated by an assignment of a buyer to a seller may be adversely affected by externalities generated by other assignments. The problem is complicated by several factors. Buyers know their own valuations and externality costs but do not know this same information for other buyers. Buyers also receive private signals correlated with the state and, consequently, the implementation problem exhibits interdependent valuations. This precludes a naive application of the VCG mechanism and to overcome this interdependency problem, we construct a two-stage mechanism. In the first stage, we exploit correlation in the firms signals about the state to induce truthful reporting of observed signals. Given that buyers are honest in stage 1, we then use a VCG-like mechanism in stage 2 that induces honest reporting of valuation and externality functions.

Suggested Citation

  • Tatiana Daddario & Richard P. McLean & Andrew Postlewaite, 2023. "An Assignment Problem with Interdependent Valuations and Externalities," Papers 2305.01477, arXiv.org.
    • Handle: RePEc:arx:papers:2305.01477
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    References listed on IDEAS

    as
    1. Richard McLean & Andrew Postlewaite, 2004. "Informational Size and Efficient Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 809-827.
    2. Che, Yeon-Koo & Kim, Jinwoo & Kojima, Fuhito, 2015. "Efficient assignment with interdependent values," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 54-86.
    3. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996. "How (Not) to Sell Nuclear Weapons," American Economic Review, American Economic Association, vol. 86(4), pages 814-829, September.
    4. Motty Perry & Philip J. Reny, 2002. "An Efficient Auction," Econometrica, Econometric Society, vol. 70(3), pages 1199-1212, May.
    5. Marcelo Ariel Fernandez & Kirill Rudov & Leeat Yariv, 2022. "Centralized Matching with Incomplete Information," American Economic Review: Insights, American Economic Association, vol. 4(1), pages 18-33, March.
    6. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    7. Roth, Alvin E., 1989. "Two-sided matching with incomplete information about others' preferences," Games and Economic Behavior, Elsevier, vol. 1(2), pages 191-209, June.
    8. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
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    More about this item

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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