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Adjusting Prices in the Many-to-many Assignment Game

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  • Marilda Sotomayor

Abstract

Starting with an initial price vector, prices are adjusted in order to eliminate the demand excess and at the same time to keep the transfers to the sellers as low as possible. In each step of the auction, to which sellers should those transfers be made (minimal overdemanded sets) is the key definition in the description of the algorithm. Such approach was previously used by several authors. We introduce a novel distinction by considering multiple sellers owing multiple identical objects and multiple buyers with a quota greater than one consuming at most one unit of each seller’s good. This distinction induces a necessarily more complicated construction of the overdemanded sets than the constructions existing in the literature, even in the simplest case of additive utilities considered here. As the previous papers, our mechanism yields the minimum competitive equilibrium price vector. A procedure to find the maximum competitive equilibrium price vector is also provided.

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File URL: http://www.brown.edu/Departments/Economics/Papers/2008/2008-13_paper.pdf
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Bibliographic Info

Paper provided by Brown University, Department of Economics in its series Working Papers with number 2008-13.

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Date of creation: 2008
Date of revision:
Handle: RePEc:bro:econwp:2008-13

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Postal: Department of Economics, Brown University, Providence, RI 02912

Related research

Keywords: matching; stable payoff; competitive equilibrium payoff; optimal stable payoff; lattice social costs; pure comparative vigilance; super-symmetric rule;

References

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  1. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521437882.
  2. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 94(4), pages 863-72, August.
  3. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 91(3), pages 461-79, June.
  4. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, Econometric Society, vol. 49(2), pages 437-50, March.
  5. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, Elsevier, vol. 92(1), pages 66-95, May.
  6. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
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Cited by:
  1. Fagebaume, Alexis & Gale, David & Sotomayor, Marilda, 2010. "A note on the multiple partners assignment game," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 388-392, July.

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