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Some game-theoretic grounds for meeting people half-way

Author

Listed:
  • José M. Jiménez Gómez

    (Universidad Politécnica de Cartagena)

  • María del Carmen Marco Gil

    (Universidad Politécnica de Cartagena)

  • Pedro Gadea Blanco

    (Universidad Politécnica de Cartagena)

Abstract
It is well known that, in distributions problems, "Fairness" rarely leads to a single viewpoint (see Young (1994) and Moulin (1988) among many others). This paper provides, in this context, interesting basis in defense of intermediate agreements when two prominent proposals, representing different sets of "Equity Principles", highlight a discrepancy in sharing resources. Specifically, we formalize such a conflicting situation by associating it with a "natural" cooperative game, called the Bifocal Distribution game, to show that both the Nucleolus, introduced by Schmeidler (1969), and the Shapley value, proposed by Shapley (1953), agree on recommending the "average of the two focal solutions". Finally, applying our analysis to bankruptcy problems, which have been analyzed extensively by Thomson (2003) and Moulin (2002), provides new "reasonable" solutions.

Suggested Citation

  • José M. Jiménez Gómez & María del Carmen Marco Gil & Pedro Gadea Blanco, 2010. "Some game-theoretic grounds for meeting people half-way," Working Papers. Serie AD 2010-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2010-04
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    References listed on IDEAS

    as
    1. Kar, Anirban & Mitra, Manipushpak & Mutuswami, Suresh, 2009. "On the coincidence of the prenucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 16-25, January.
    2. Cuberes, David & Dougan, William, 2009. "How Endogenous Is Money? Evidence from a New Microeconomic Estimate," MPRA Paper 17744, University Library of Munich, Germany.
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    7. Maliar, Lilia & Maliar, Serguei & Valli, Fernando, 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 42-49, January.
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    10. Menner, Martin, 2007. "The role of search frictions for output and inflation dynamics: a Bayesian assessment," UC3M Working papers. Economics we076235, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    12. Lídia Farré & Roger Klein & Francis Vella, 2012. "Does Increasing Parents’ Schooling Raise the Schooling of the Next Generation? Evidence Based on Conditional Second Moments," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(5), pages 676-690, October.
    13. José M. Jiménez Gómez & María del Carmen Marco Gil & Pedro Gadea Blanco, 2010. "Some game-theoretic grounds for meeting people half-way," Working Papers. Serie AD 2010-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    14. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. José J. Sempere Monerris & Rafael Moner Colonques & Amparo Urbano Salvador, 2010. "Trade liberalization in vertically related markets," Working Papers. Serie AD 2010-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. José M. Jiménez Gómez & María del Carmen Marco Gil & Pedro Gadea Blanco, 2010. "Some game-theoretic grounds for meeting people half-way," Working Papers. Serie AD 2010-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    2. Giménez Gómez, José M. (José Manuel) & Osório, António (António Miguel) & Peris, Josep E., 2014. "Compromise solutions for bankruptcy situations: a note," Working Papers 2072/237592, Universitat Rovira i Virgili, Department of Economics.
    3. José-Manuel Giménez-Gómez, 2014. "A Way to Play Claims Problems," Group Decision and Negotiation, Springer, vol. 23(3), pages 617-627, May.
    4. Pedro Gadea-Blanco & José-Manuel Giménez-Gómez & M. Carmen Marco-Gil, 2016. "Compromising in bifocal distribution games: the average value," Theory and Decision, Springer, vol. 81(3), pages 449-465, September.

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    More about this item

    Keywords

    distribution problems; bankruptcy; cooperative games; nucleolus; Shapley value; Lorenz criterion.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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