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Some game-theoretic grounds for meeting people half-way

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  • 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.

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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2010-04.

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Length: 26 pages
Date of creation: Mar 2010
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2010-04

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

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References

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  1. Anirban Kar & Manipushpak Mitra & Suresh Mutuswami, 2005. "On the coincidence of the Prenucleolus and the Shapley Value," Economics Discussion Papers 599, University of Essex, Department of Economics.
  2. Iñigo Iturbe-Ormaetxe Kortajarene & Marisa Hidalgo, 2009. "Should we transfer resources from college to basic education?," Working Papers. Serie AD 2009-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. 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.
  4. Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(1), pages 1-41, July.
  5. Antoni Cunyat & Randolph Sloof, 2008. "Employee Types and Endogenous Organizational Design," Tinbergen Institute Discussion Papers 08-019/1, Tinbergen Institute.
  6. Cuberes, David & Dougan, William, 2009. "How Endogenous Is Money? Evidence from a New Microeconomic Estimate," MPRA Paper 17744, University Library of Munich, Germany.
  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.
  8. 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.
  9. 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).
  10. Elisabeth Naeve-Steinweg, 1999. "A note on van Damme's mechanism," Review of Economic Design, Springer, vol. 4(2), pages 179-187.
  11. Martin Menner, 2007. "The role of search frictions for output and inflation dynamics: a Bayesian assessment," Economics Working Papers we076235, Universidad Carlos III, Departamento de Economía.
  12. Gadea-Blanco, Pedro & Giménez-Gómez, José Manuel & Marco-Gil, María del Carmen, 2013. "Some game-theoretic grounds for meeting people half-way," Working Papers 2072/220217, Universitat Rovira i Virgili, Department of Economics.
  13. 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, vol. 16(1), pages 60-61, July.
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Cited by:
  1. Gadea-Blanco, Pedro & Giménez-Gómez, José Manuel & Marco-Gil, María del Carmen, 2013. "Some game-theoretic grounds for meeting people half-way," Working Papers 2072/220217, Universitat Rovira i Virgili, Department of Economics.
  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. Giménez-Gómez, José Manuel, 2011. "A way to play bankruptcy problems," Working Papers 2072/169781, Universitat Rovira i Virgili, Department of Economics.

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