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Competitive Equilibrium with Indivisibilities

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  • Jinpeng Ma

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    (Economics, Rutgers University, Camden, NJ 08102)

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    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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    Bibliographic Info

    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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    References

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    1. Martine Quinzii, 1982. "Core and Competitive Equilibria with Indivisibilities," Cowles Foundation Discussion Papers 644, Cowles Foundation for Research in Economics, Yale University.
    2. 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.
    3. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    4. Kaneko, Mamoru, 1983. "Housing markets with indivisibilities," Journal of Urban Economics, Elsevier, vol. 13(1), pages 22-50, January.
    5. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
    6. Gul, F. & Stacchetti, E., 1997. "Walrasian Equilibrium Without Complementarities," Papers 97-03, Michigan - Center for Research on Economic & Social Theory.
    7. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July.
    8. 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.
    9. 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.
    10. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
    11. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    12. Ellickson,Bryan, 1994. "Competitive Equilibrium," Cambridge Books, Cambridge University Press, number 9780521319881, October.
    13. 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.
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    Cited by:
    1. Ma, Jinpeng & Nie, Fusheng, 2003. "Walrasian equilibrium in an exchange economy with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 159-192, October.
    2. Jinpeng Ma, 1998. "Job Matching and Coalition Formation with Utility or Disutility of Co-workers," Discussion Papers 1230, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Yang, Yi-You, 2012. "Free disposal, monotonicity and equilibrium," MPRA Paper 42585, University Library of Munich, Germany.
    4. 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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