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Core and competitive equilibria with indivisibilities

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Abstract

The paper presents a model of an exchange economy with indivisible goods and money. There are a finite number of agents, each one initially endowed with a certain amount of money and at most one indivisible good. Each agent is assumed to have no use for more than one indivisible good. It is proved that the core of the economy is nonempty. If utility functions are increasing in money, and if the initial resources in money are in some sense “sufficient” the core allocations coincide with the competitive equilibrium allocations.

With restrictions on the set of feasible allocations, the same model is used to prove the existence of stable solutions in the generalized “marriage problem”. However it is shown that, even if money enters the model, these solutions cannot generally be obtained as competitive equilibria.

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References

  • Crawford, V.P., andE.M. Knoer: Job Matching with Heterogenous Firms and Workers. Econometrica49, 1981, 437–450.

    Google Scholar 

  • Gale, D., andL.S. Shapley: College Admissions and the Stability of Marriage. American Mathematical Monthly69, 1962, 9–15.

    Google Scholar 

  • Kaneko, M.: The Central Assignment Game and the Assignment Markets. Journal of Mathematical Economics10, 1982, 1483–1504.

    Google Scholar 

  • —: Housing Markets with Indivisibilities. Journal of Urban Economics13, 1983, 22–50.

    Google Scholar 

  • Kelso, A.S., andV.P. Crawford: Job Matching Coalition Formation and Gross Substitutes. Econometrica50, 1982, 1483–1504.

    Google Scholar 

  • Roth, A.E., andA. Postlewaite: Weak Versus Strong Domination in a Market with Indivisible Goods. Journal of Mathematical Economics4, 1977, 131–137.

    Google Scholar 

  • Scarf, H.E.: The Core of ann-person Game. Econometrica35, 1967, 50–69.

    Google Scholar 

  • Shapley, L.S.: On Balanced Sets and Cores. The Rand Corporation, Memorandum RM-4601-PR, June 1965.

  • Shapley, L.S., andH.E. Scarf: On Cores and Indivisibility. Journal of Mathematical Economics1, 1974, 23–28.

    Google Scholar 

  • Shapley, L.S., andM. Shubik: The Assignment Game I: The Core. International Journal of Game Theory1, 1972, 111–130.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Laboratoire d'Econométrie de l'Ecole Polytechnique, Université d'Aix-Marseille III, 1 Rue Descartes, 75230, Paris, France

    M. Quinzii

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  1. M. Quinzii
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Additional information

Part of this work was done in the winter 1982 when I was visiting the Cowles Foundation for Research in Economics.

I am greatly indebted to Mamoru Kaneko who introduced me to the subject and helped me in many discussions. I have also a large debt to David Gale who took an active part in the completion of the last part of the paper.

This work is partially sponsored by the Department of The Navy, Contract N00014-77-C-0518 issued by the Office of Naval Research under Contract Authority NR 047-006.

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Quinzii, M. Core and competitive equilibria with indivisibilities. Int J Game Theory 13, 41–60 (1984). https://doi.org/10.1007/BF01769864

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  • DOI: https://doi.org/10.1007/BF01769864

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