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Assignment Messages and Exchanges


  • Paul Milgrom


"Assignment messages" are maximally general messages to describe substitutable preferences by means of a linear program. With "integer assignment messages," there exist integer-valued Walrasian allocations, extending a result of Lloyd S. Shapley and Martin Shubik (1971). Any pure Nash equilibrium profile of the Walrasian mechanism with participants limited to assignment messages is also a Nash equilibrium of the unrestricted Walrasian mechanism. Assignment exchanges are generalizations of single-product double auctions and are related to ascending multi-product clock auctions and the Vickrey mechanism. Assignment messages also have additional applications in mechanism design. (JEL D44, D82)

Suggested Citation

  • Paul Milgrom, 2009. "Assignment Messages and Exchanges," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 95-113, August.
  • Handle: RePEc:aea:aejmic:v:1:y:2009:i:2:p:95-113 Note: DOI: 10.1257/mic.1.2.95

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    References listed on IDEAS

    1. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    2. Lawrence M. Ausubel & Peter Cramton, 2004. "Auctioning Many Divisible Goods," Journal of the European Economic Association, MIT Press, vol. 2(2-3), pages 480-493, 04/05.
    3. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
    4. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, March.
    5. Robert Wilson, 1979. "Auctions of Shares," The Quarterly Journal of Economics, Oxford University Press, vol. 93(4), pages 675-689.
    6. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    7. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    8. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    9. Milgrom, Paul & Strulovici, Bruno, 2009. "Substitute goods, auctions, and equilibrium," Journal of Economic Theory, Elsevier, vol. 144(1), pages 212-247, January.
    10. Peter Cramton & Yoav Shoham & Richard Steinberg (ed.), 2006. "Combinatorial Auctions," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033429, July.
    11. Nisan, Noam & Segal, Ilya, 2006. "The communication requirements of efficient allocations and supporting prices," Journal of Economic Theory, Elsevier, vol. 129(1), pages 192-224, July.
    12. Peter Cramton & Yoav Shoham & Richard Steinberg, 2004. "Combinatorial Auctions," Papers of Peter Cramton 04mit, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
    13. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    14. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    15. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
    16. Lawrence M. Ausubel, 2004. "An Efficient Ascending-Bid Auction for Multiple Objects," American Economic Review, American Economic Association, vol. 94(5), pages 1452-1475, December.
    17. Ilan Kremer & Kjell G. Nyborg, 2004. "Divisible-Good Auctions: The Role of Allocation Rules," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 147-159, Spring.
    18. Paul Milgrom, 2007. "Package Auctions and Exchanges," Econometrica, Econometric Society, vol. 75(4), pages 935-965, July.
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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

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design


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