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Assignment Messages and Exchanges

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  • Paul Milgrom

    () (Stanford University)

Abstract

“Assignment messages” are messages that parameterize substitutable preferences using a particular linear program. An “assignment exchange” is a simplified Walrasian exchange in which participants are restricted to report only assignment messages. Any pure Nash or e-Nash equilibrium of the simplified mechanism is a Nash or e-Nash equilibrium of the Walrasian mechanism before simplification. With a further restriction to basic assignment messages, the exchange yields integer-valued allocations, thus generalizing the Shapley-Shubik assignment mechanism. Connections are reported between assignment exchanges and ascending multi-product clock auctions, double auctions for a single product, and Vickrey auctions. Applications include some cases of Leontieff complements.

Suggested Citation

  • Paul Milgrom, 2008. "Assignment Messages and Exchanges," Discussion Papers 08-014, Stanford Institute for Economic Policy Research.
  • Handle: RePEc:sip:dpaper:08-014
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Martínez, Ruth & Massó, Jordi & Neme, Alejandro & Oviedo, Jorge, 2012. "On the invariance of the set of Core matchings with respect to preference profiles," Games and Economic Behavior, Elsevier, vol. 74(2), pages 588-600.
    2. Milgrom, Paul, 2010. "Simplified mechanisms with an application to sponsored-search auctions," Games and Economic Behavior, Elsevier, vol. 70(1), pages 62-70, September.
    3. Goto, Masahiro & Kojima, Fuhito & Kurata, Ryoji & Tamura, Akihisa & Yokoo, Makoto, 2015. "Designing Matching Mechanisms under General Distributional Constraints," MPRA Paper 64000, University Library of Munich, Germany.
    4. Matías Núñez & Jean Laslier, 2014. "Preference intensity representation: strategic overstating in large elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 313-340, February.
    5. McLaughlin, Kevin & Friedman, Daniel, 2016. "Online ad auctions: An experiment," Discussion Papers, Research Professorship Market Design: Theory and Pragmatics SP II 2016-501, Social Science Research Center Berlin (WZB).
    6. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.
    7. repec:the:publsh:2717 is not listed on IDEAS
    8. Massó, Jordi & Neme, Alejandro, 2014. "On cooperative solutions of a generalized assignment game: Limit theorems to the set of competitive equilibria," Journal of Economic Theory, Elsevier, vol. 154(C), pages 187-215.
    9. Aytek Erdil & Paul Klemperer, 2010. "A New Payment Rule for Core-Selecting Package Auctions," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 537-547, 04-05.
    10. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
    11. Kos, Nenad, 2014. "Asking questions," Games and Economic Behavior, Elsevier, vol. 87(C), pages 642-650.

    More about this item

    Keywords

    mechanism design; market design; auctions; Shapley-Shubik;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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