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Assignment Messages and Exchanges

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  • Paul Milgrom

Abstract

"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)

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File URL: http://www.aeaweb.org/articles.php?doi=10.1257/mic.1.2.95
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Bibliographic Info

Article provided by American Economic Association in its journal American Economic Journal: Microeconomics.

Volume (Year): 1 (2009)
Issue (Month): 2 (August)
Pages: 95-113

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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

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  1. Lawrence M. Ausubel & Peter Cramton, 2004. "Auctioning Many Divisible Goods," Papers of Peter Cramton 04jeea, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
  2. Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc.
  3. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
  4. 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.
  5. Milgrom, Paul & Strulovici, Bruno, 2009. "Substitute goods, auctions, and equilibrium," Journal of Economic Theory, Elsevier, vol. 144(1), pages 212-247, January.
  6. Paul Milgrom, . "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Working Papers 98002, Stanford University, Department of Economics.
  7. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
  8. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  9. 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.
  10. Peter Cramton & Yoav Shoham & Richard Steinberg (ed.), 2006. "Combinatorial Auctions," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033429.
  11. Paul Milgrom, 2007. "Package Auctions and Exchanges," Econometrica, Econometric Society, vol. 75(4), pages 935-965, 07.
  12. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, October.
  13. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  14. 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.
  15. Wilson, Robert, 1979. "Auctions of Shares," The Quarterly Journal of Economics, MIT Press, vol. 93(4), pages 675-89, November.
  16. 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.
  17. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
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Citations

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Cited by:
  1. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.
  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. Matias Nunez & Jean-Francois Laslier, 2013. "Preference Intensity Representation : Strategic Overstating in Large Elections," Post-Print hal-00917099, HAL.
  4. Paul Klemperer & Aytek Erdil, 2009. "A New Payment Rule for Core-Selecting Package Auctions," Economics Series Working Papers 2009-W11, University of Oxford, Department of Economics.
  5. Jordi Massó & Alejandro Neme, 2010. "On Cooperative Solutions of a Generalized Assignment Game: Limit Theorems to the Set of Competitive Equilibria," UFAE and IAE Working Papers 810.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
  7. Ruth Martínez & Jordi Massó & Alejandro Neme & Jorge Oviedo, 2009. "On the Invariance of the Set of Core Matchings with Respect to Preference Profiles," Working Papers 390, Barcelona Graduate School of Economics.

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