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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
    as

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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.
    3. Marisa Hidalgo-Hidalgo & Iñigo Iturbe-Ormaetxe, 2012. "Should we transfer resources from college to basic education?," Journal of Economics, Springer, vol. 105(1), pages 1-27, January.
    4. Stefano Moretti & Fioravante Patrone, 2008. "Rejoinder on: Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 60-61, July.
    5. Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 1-41, July.
    6. 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.
    7. Cunyat, Antoni & Sloof, Randolph, 2011. "Employee types and endogenous organizational design: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 80(3), pages 553-573.
    8. Elisabeth Naeve-Steinweg, 1999. "A note on van Damme's mechanism," Review of Economic Design, Springer;Society for Economic Design, vol. 4(2), pages 179-187.
    9. 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.
    10. 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.
    11. 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.
    12. 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).
    13. 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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    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 & António Osório & Josep E. Peris, 2016. "Bankruptcy problems with two references: an impartial compromise," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 131-142, April.
    4. repec:spr:grdene:v:23:y:2014:i:3:d:10.1007_s10726-013-9347-5 is not listed on IDEAS
    5. 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.

    More about this item

    Keywords

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

    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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