IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/8444.html
   My bibliography  Save this paper

Envy-free solutions, Non-linear equilibrium and Egalitarian-equivalence for the Package Assignment Problem

Author

Listed:
  • Lahiri, Somdeb

Abstract

The first result in this paper says that given any efficient non-monetary allocation there is a balanced vector of transfers so that the resulting allocation is fair. The second result here says that given any efficient non-monetary allocation there is a pricing function defined on consumption bundles and a balanced vector of transfers so that they together form a non-linear market equilibrium. The first result is used to establish the second. Subsequently we prove the existence of egalitarian equivalent solutions for package assignment problems and shows that they satisfy the “fair share guaranteed” property.

Suggested Citation

  • Lahiri, Somdeb, 2008. "Envy-free solutions, Non-linear equilibrium and Egalitarian-equivalence for the Package Assignment Problem," MPRA Paper 8444, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:8444
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/8444/1/MPRA_paper_8444.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/8498/1/MPRA_paper_8498.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Gul, F. & Stacchetti, E., 1997. "Walrasian Equilibrium Without Complementarities," Papers 97-03, Michigan - Center for Research on Economic & Social Theory.
    3. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    4. 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.
    5. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(4), pages 671-687.
    6. Carmen BeviÂ, 1998. "Fair allocation in a general model with indivisible goods," Review of Economic Design, Springer;Society for Economic Design, vol. 3(3), pages 195-213.
    7. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    2. Dall’Aglio, Marco, 2023. "Fair division of goods in the shadow of market values," European Journal of Operational Research, Elsevier, vol. 307(2), pages 785-801.
    3. Youngsub Chun, 2006. "No-envy in queueing problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 151-162, September.
    4. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    5. Peter R. Wurman & Michael P. Wellman, 1999. "Equilibrium Prices in Bundle Auctions," Working Papers 99-09-064, Santa Fe Institute.
    6. Jinpeng Ma, 1997. "English Auctions and Walrasian Equilibria with Multiple Objects: a dynamic approach," Departmental Working Papers 199702, Rutgers University, Department of Economics.
    7. Proano, Ruben A. & Jacobson, Sheldon H. & Zhang, Wenbo, 2012. "Making combination vaccines more accessible to low-income countries: The antigen bundle pricing problem," Omega, Elsevier, vol. 40(1), pages 53-64, January.
    8. Arribas, I. & Urbano, A., 2017. "Multiproduct trading with a common agent under complete information: Existence and characterization of Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 167(C), pages 14-38.
    9. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2014. "Egalitarian equivalence and strategyproofness in the queueing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 425-442, June.
    10. Lukas Hümbs & Alexander Martin & Lars Schewe, 2022. "Exploiting complete linear descriptions for decentralized power market problems with integralities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 451-474, June.
    11. Meertens, Marc & Potters, Jos & Reijnierse, Hans, 2002. "Envy-free and Pareto efficient allocations in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 223-233, December.
    12. Martin Bichler & Johannes Knörr & Felipe Maldonado, 2023. "Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response," Information Systems Research, INFORMS, vol. 34(2), pages 652-675, June.
    13. Watts, Alison, 1999. "Cooperative production: a comparison of lower and upper bounds," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 317-331, November.
    14. Arribas, Ivan & Urbano, Amparo, 2005. "Nash equilibria in a model of multiproduct price competition: an assignment problem," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 351-385, April.
    15. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
    16. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    17. Zhiling Guo & Gary J. Koehler & Andrew B. Whinston, 2012. "A Computational Analysis of Bundle Trading Markets Design for Distributed Resource Allocation," Information Systems Research, INFORMS, vol. 23(3-part-1), pages 823-843, September.
    18. Chun, Youngsub & Mitra, Manipushpak & Mutuswami, Suresh, 2019. "Egalitarianism in the queueing problem," Journal of Mathematical Economics, Elsevier, vol. 81(C), pages 48-56.
    19. Sakai, Toyotaka, 2007. "Fairness and implementability in allocation of indivisible objects with monetary compensations," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 549-563, June.
    20. Ravi Bapna & Paulo Goes & Alok Gupta, 2005. "Pricing and Allocation for Quality-Differentiated Online Services," Management Science, INFORMS, vol. 51(7), pages 1141-1150, July.

    More about this item

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:8444. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.