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A way to play bankruptcy problems


  • Giménez-Gómez, José Manuel


The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

Suggested Citation

  • Giménez-Gómez, José Manuel, 2011. "A way to play bankruptcy problems," Working Papers 2072/169781, Universitat Rovira i Virgili, Department of Economics.
  • Handle: RePEc:urv:wpaper:2072/169781

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    References listed on IDEAS

    1. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 547-569, August.
    2. Dagan, Nir & Serrano, Roberto & Volij, Oscar, 1997. "A Noncooperative View of Consistent Bankruptcy Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 55-72, January.
    3. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    4. Ignacio García-Jurado & Julio González-Díaz & Antonio Villar, 2006. "A Non-cooperative Approach to Bankruptcy Problems," Spanish Economic Review, Springer;Spanish Economic Association, vol. 8(3), pages 189-197, September.
    5. Cowell, F.A., 2000. "Measurement of inequality," Handbook of Income Distribution,in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 2, pages 87-166 Elsevier.
    6. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 791-807, November.
    7. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
    8. Eric van Damme, 1984. "The Nash Bargaining Solution is Optimal," Discussion Papers 597, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. 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.
    10. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    11. Chun, Youngsub, 1989. "A noncooperative justification for egalitarian surplus sharing," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 245-261, June.
    12. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    13. Damme, Eric van, 1986. "The Nash bargaining solution is optimal," Journal of Economic Theory, Elsevier, vol. 38(1), pages 78-100, February.
    14. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    15. Josep Enric Peris Ferrando & Begoña Subiza & María del Carmen Marco, 1995. "A Mechanism For Meta-Bargaining Problems," Working Papers. Serie AD 1995-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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    More about this item


    Fallida; Jocs cooperatius; Economia del benestar; Elecció social; 33 - Economia;

    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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