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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.

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Bibliographic Info

Paper provided by Stanford Institute for Economic Policy Research in its series Discussion Papers with number 08-014.

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Date of creation: Dec 2008
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Handle: RePEc:sip:dpaper:08-014

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

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References

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  1. 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.
  2. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, April.
  3. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  4. 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.
  5. 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.
  6. 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.
  7. Milgrom, Paul & Strulovici, Bruno, 2009. "Substitute goods, auctions, and equilibrium," Journal of Economic Theory, Elsevier, vol. 144(1), pages 212-247, January.
  8. 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.
  9. Peter Cramton & Yoav Shoham & Richard Steinberg (ed.), 2006. "Combinatorial Auctions," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033429, December.
  10. 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.
  11. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
  12. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  13. 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.
  14. Wilson, Robert, 1979. "Auctions of Shares," The Quarterly Journal of Economics, MIT Press, vol. 93(4), pages 675-89, November.
  15. Paul Milgrom, 2007. "Package Auctions and Exchanges," Econometrica, Econometric Society, vol. 75(4), pages 935-965, 07.
  16. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  17. 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.
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Citations

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Cited by:
  1. Milgrom, Paul, 2010. "Simplified mechanisms with an application to sponsored-search auctions," Games and Economic Behavior, Elsevier, vol. 70(1), pages 62-70, September.
  2. Ruth Martínez & Jordi Massó & Alejandro Neme & Jorge Oviedo, 2009. "On the Invariance of the Set of Core Matchings with Respect to Preference Profiles," UFAE and IAE Working Papers 803.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  3. Aytek Erdil & Paul Klemperer, 2009. "A New Payment Rule for Core-Selecting Package Auctions," Economics Papers 2009-W11, Economics Group, Nuffield College, University of Oxford.
  4. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
  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. Matias Nunez & Jean-Francois Laslier, 2013. "Preference Intensity Representation : Strategic Overstating in Large Elections," Post-Print hal-00917099, HAL.
  7. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.

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