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Competitive Equilibrium with Indivisibilities

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  • Jinpeng Ma

    ()

    (Economics, Rutgers University, Camden, NJ 08102)

Abstract

This paper studies an exchange economy with a finite number of agents in which each agent is initially endowed with a finite number of (personalized) indivisible commodities. We observe that the core equivalence theorem may not hold for this economy when the coalitional form game is generated in the standard manner. We provide an alternative definition of the coalitional form game to resolve this problem so that the balancedness of the new defined game provides a useful necessary and sufficient condition for the existence of competitive equilibrium for the original economy. We also observe that the nice strategy proof property of the minimum competitive price mechanism in the assignment problem and the Vickrey auction model does not carry over to the above economy. We show that examples of exchange economies exist for which no competitive price mechanism is individually (coalitionally) strategy proof.

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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 199809.

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Date of creation: 12 Apr 1998
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Handle: RePEc:rut:rutres:199809
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Keywords: competitive equilibrium;

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Find related papers by JEL classification:
  • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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  1. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
  2. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  3. Mamoru Kaneko, 1980. "The Central Assignment Game and the Assignment Markets," Cowles Foundation Discussion Papers 563, Cowles Foundation for Research in Economics, Yale University.
  4. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
  5. Tjalling C. Koopmans & Martin J. Beckmann, 1955. "Assignment Problems and the Location of Economic Activities," Cowles Foundation Discussion Papers 4, Cowles Foundation for Research in Economics, Yale University.
  6. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  7. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-79, June.
  8. Gul, F. & Stacchetti, E., 1997. "Walrasian Equilibrium Without Complementarities," Papers 97-03, Michigan - Center for Research on Economic & Social Theory.
  9. 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.
  10. repec:cup:cbooks:9780521319881 is not listed on IDEAS
  11. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers 644, Cowles Foundation for Research in Economics, Yale University.
  12. Kaneko, Mamoru, 1983. "Housing markets with indivisibilities," Journal of Urban Economics, Elsevier, vol. 13(1), pages 22-50, January.
  13. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July.
  14. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  15. Kaneko, Mamoru & Yamamoto, Yoshitsugu, 1986. "The existence and computation of competitive equilibria in markets with an indivisible commodity," Journal of Economic Theory, Elsevier, vol. 38(1), pages 118-136, February.
  16. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
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Cited by:

  1. Koshevoy, G.A. & Talman, A.J.J., 2006. "Competitive Equilibria in Economies with Multiple Divisible and Indivisible Commodities and No Money," Discussion Paper 2006-51, Tilburg University, Center for Economic Research.
  2. Koshevoy, G.A. & Talman, A.J.J., 2002. "Competitive Equilibria in Economies with Multiple Divisible and Multiple Divisible Commodities," Discussion Paper 2002-71, Tilburg University, Center for Economic Research.
  3. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2002. "Existence and welfare properties of equilibrium in an exchange economy with multiple divisible and indivisible commodities and linear production," Other publications TiSEM 5a5610bf-4f85-4a25-963c-c, School of Economics and Management.
  4. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 1999. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible, Indivisible Commodities and Linear Production Technologies," Discussion Paper 1999-76, Tilburg University, Center for Economic Research.
  5. Ma, Jinpeng, 2001. "Job Matching and Coalition Formation with Utility or Disutility of Co-workers," Games and Economic Behavior, Elsevier, vol. 34(1), pages 83-103, January.
  6. Yang, Zaifu, 2003. "A competitive market model for indivisible commodities," Economics Letters, Elsevier, vol. 78(1), pages 41-47, January.
  7. Yang, Yi-You, 2012. "Free disposal, monotonicity and equilibrium," MPRA Paper 42585, University Library of Munich, Germany.
  8. Jinpeng Ma, 1997. "English Auctions and Walrasian Equilibria with Multiple Objects: a dynamic approach," Departmental Working Papers 199702, Rutgers University, Department of Economics.
  9. Yang, Yi-You, 2013. "Competitive equilibrium for indivisible objects," MPRA Paper 57637, University Library of Munich, Germany, revised 28 Jul 2014.
  10. Ma, Jinpeng & Nie, Fusheng, 2003. "Walrasian equilibrium in an exchange economy with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 159-192, October.
  11. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2002. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies," Journal of Economic Theory, Elsevier, vol. 103(2), pages 411-428, April.
  12. Jinpeng Ma, 1997. "Walrasian Equilibria in a Production Economy with Indivisibilities," Departmental Working Papers 199712, Rutgers University, Department of Economics.
  13. Akiyoshi Shioura & Zaifu Yang, 2013. "Equilibrium, Auction, Multiple Substitutes and Complements," Discussion Papers 13/17, Department of Economics, University of York.

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