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

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  • 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
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    References listed on IDEAS

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    1. Rader, Trout, 1972. "Theory of General Economic Equilibrium," Elsevier Monographs, Elsevier, edition 1, number 9780125750400.
    2. Chambers,Robert G. & Quiggin,John, 2000. "Uncertainty, Production, Choice, and Agency," Cambridge Books, Cambridge University Press, number 9780521785235, November.
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    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.

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    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

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