IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v09y2007i03ns0219198907001527.html
   My bibliography  Save this article

A Note On Luenberger'S Zero-Maximum Principle For Core Allocations

Author

Listed:
  • JEAN-MICHEL COURTAULT

    (L.I.B.R.E., Faculté de Droit et de Sciences Economiques, Université de Franche-Comté, 45 D avenue de l'observatoire, 25030, Besançon cedex, France)

  • BERTRAND CRETTEZ

    (L.I.B.R.E., Université de Franche-Comté, France)

  • NAILA HAYEK

    (L.I.B.R.E., Université de Franche-Comté, and CERMSEM, Université de Paris I, France)

Abstract

In this note, we state a zero-maximum principle for core allocations, a result which was foreseen by Luenberger (1995). We prove a generalization of the first-zero maximum theorem of Luenberger. Roughly said, an allocation is in the core if for every coalition, the sum of individual benefit functions is non-positive. We also provide some partial converses which give a generalization of the second-zero maximum theorem of Luenberger.

Suggested Citation

  • Jean-Michel Courtault & Bertrand Crettez & Naila Hayek, 2007. "A Note On Luenberger'S Zero-Maximum Principle For Core Allocations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 453-460.
    • Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:03:n:s0219198907001527
    DOI: 10.1142/S0219198907001527
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198907001527
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198907001527?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chambers,Robert G. & Quiggin,John, 2000. "Uncertainty, Production, Choice, and Agency," Cambridge Books, Cambridge University Press, number 9780521785235.
    2. Rader, Trout, 1972. "Theory of General Economic Equilibrium," Elsevier Monographs, Elsevier, edition 1, number 9780125750400.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jean-Michel Courtault & Bertrand Crettez & Naïla Hayek, 2005. "Allais's Trading Process And The Dynamic Evolution of an OLG Markets Economy," Post-Print halshs-00448184, HAL.
    2. Raphaël Giraud, 2012. "Money matters: an axiomatic theory of the endowment effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 303-339, June.
    3. Juan Aparicio & Jesus T. Pastor, 2012. "Benefit function and individual preferences. A generalization of the zero-maximum principle," Economics and Business Letters, Oviedo University Press, vol. 1(1), pages 12-20.

    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. del Mercato, Elena L. & Nguyen, Van-Quy, 2023. "Sufficient conditions for a “simple” decentralization with consumption externalities," Journal of Economic Theory, Elsevier, vol. 209(C).
    2. Robert G. Chambers & John Quiggin, 2007. "Dual Approaches to the Analysis of Risk Aversion," Economica, London School of Economics and Political Science, vol. 74(294), pages 189-213, May.
    3. Rasmussen, Svend, 2003. "Criteria for optimal production under uncertainty. The state-contingent approach," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 47(4), pages 1-30.
    4. Robert Becker & Stefano Bosi & Cuong Van & Thomas Seegmuller, 2015. "On existence and bubbles of Ramsey equilibrium with borrowing constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 329-353, February.
    5. Macedo, Pedro & Scotto, Manuel, 2014. "Cross-entropy estimation in technical efficiency analysis," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 124-130.
    6. Bouali Guesmi & Teresa Serra & Allen Featherstone, 2015. "Technical efficiency of Kansas arable crop farms: a local maximum likelihood approach," Agricultural Economics, International Association of Agricultural Economists, vol. 46(6), pages 703-713, November.
    7. John Quiggin, 2022. "Production under uncertainty and choice under uncertainty in the emergence of generalized expected utility theory," Theory and Decision, Springer, vol. 92(3), pages 717-729, April.
    8. Robert G. Chambers & Margarita Genius & Vangelis Tzouvelekas, 2021. "Invariant Risk Preferences and Supply Response under Price Risk," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(5), pages 1802-1819, October.
    9. Sriram Shankar & John Quiggin, 2013. "Production under uncertainty: a simulation study," Journal of Productivity Analysis, Springer, vol. 39(3), pages 207-215, June.
    10. Quiggin, John & Adamson, David & Chambers, Sarah & Schrobback, Peggy, 2009. "Climate change, mitigation and adaptation: the case of the Murray-Darling Basin in Australia," Risk and Sustainable Management Group Working Papers 149878, University of Queensland, School of Economics.
    11. Adamson, David & Mallawaarachchi, Thilak & Quiggin, John, 2004. "Modelling basin level allocation of water in the Murray Darling Basin in a world of uncertainty," Risk and Sustainable Management Group Working Papers 149844, University of Queensland, School of Economics.
    12. Robert G. Chambers & John Quiggin, 2005. "Incentives and Standards in Agency Contracts," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(2), pages 201-228, May.
    13. Adamson, David & Mallawaarachchi, Thilak & Quiggin, John C., 2007. "Water use and salinity in the Murray–Darling Basin: A state-contingent model," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 51(3), pages 1-19.
    14. Shankar, Sriram, 2012. "Production economics in the presence of risk," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 56(4), pages 1-24, December.
    15. repec:ipg:wpaper:4 is not listed on IDEAS
    16. Chambers, Robert G. & Quiggin, John C., 2002. "Resource Allocation And Asset Pricing," Working Papers 28594, University of Maryland, Department of Agricultural and Resource Economics.
    17. Eldon V. Ball & Ricardo Cavazos & Jeffrey T. LaFrance & Rulon Pope & Jesse Tack, 2010. "Aggregation and Arbitrage in Joint Production," Monash Economics Working Papers archive-22, Monash University, Department of Economics.
    18. Shankar, Sriram, 2015. "Efficiency analysis under uncertainty: a simulation study," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 59(2), April.
    19. Chambers, Robert G. & Quiggin, John, 2009. "Separability of stochastic production decisions from producer risk preferences in the presence of financial markets," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 730-737, December.
    20. Orea, Luis, 2019. "The Econometric Measurement of Firms’ Efficiency," Efficiency Series Papers 2019/02, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    21. Serra, Teresa & Chambers, Robert G. & Oude Lansink, Alfons, 2014. "Measuring technical and environmental efficiency in a state-contingent technology," European Journal of Operational Research, Elsevier, vol. 236(2), pages 706-717.

    More about this item

    Keywords

    Zero-maximum principle; benefit functions; distributable surplus; core; JEL Classification Numbers: D51; JEL Classification Numbers: D61;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    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:wsi:igtrxx:v:09:y:2007:i:03:n:s0219198907001527. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.