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A strategic justification of the Talmud rule based on lower and upper bounds

Author

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  • Juan D. Moreno-Ternero

    (Universidad Pablo de Olavide)

  • Min-Hung Tsay

    (National Chung Cheng University)

  • Chun-Hsien Yeh

    (Institute of Economics, Academia Sinica
    Chung-hua Institute for Economic Research)

Abstract

We follow the Nash program to provide a new strategic justification of the Talmud rule in bankruptcy problems. The design of our game is based on a focal axiomatization of the rule, which combines consistency with meaningful lower and upper bounds to all creditors. Our game actually considers bilateral negotiations, inspired by those bounds, which are extended to an arbitrary number of creditors, by means of consistency.

Suggested Citation

  • Juan D. Moreno-Ternero & Min-Hung Tsay & Chun-Hsien Yeh, 2020. "A strategic justification of the Talmud rule based on lower and upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1045-1057, December.
  • Handle: RePEc:spr:jogath:v:49:y:2020:i:4:d:10.1007_s00182-020-00727-z
    DOI: 10.1007/s00182-020-00727-z
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    1. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. 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.
    4. Moreno-Ternero, Juan D., 2011. "Voting over piece-wise linear tax methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 29-36, January.
    5. Juan J. Vidal-Puga, 2004. "Bargaining with commitments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 129-144, January.
    6. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    7. Serrano, Roberto, 1995. "Strategic bargaining, surplus sharing problems and the nucleolus," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 319-329.
    8. Diego Dominguez & William Thomson, 2006. "A new solution to the problem of adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 283-307, June.
    9. Ju, Yuan & Chun, Youngsub & van den Brink, René, 2014. "Auctioning and selling positions: A non-cooperative approach to queueing conflicts," Journal of Economic Theory, Elsevier, vol. 153(C), pages 33-45.
    10. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    11. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    12. Tsay, Min-Hung & Yeh, Chun-Hsien, 2019. "Relations among the central rules in bankruptcy problems: A strategic perspective," Games and Economic Behavior, Elsevier, vol. 113(C), pages 515-532.
    13. Juan D. Moreno-Ternero, 2017. "A Talmudic approach to bankruptcy problems," LIDAM Reprints CORE 2914, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Juan Moreno-Ternero & Antonio Villar, 2006. "New characterizations of a classical bankruptcy rule," Review of Economic Design, Springer;Society for Economic Design, vol. 10(2), pages 73-84, August.
    15. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2012. "Axiomatic and strategic justifications for the constrained equal benefits rule in the airport problem," Games and Economic Behavior, Elsevier, vol. 75(1), pages 185-197.
    16. Youngsub Chun & Cheng-Cheng Hu & Chun-Hsien Yeh, 2017. "A Strategic Implementation of the Shapley Value for the Nested Cost-Sharing Problem," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(1), pages 219-233, February.
    17. Yeh, Chun-Hsien, 2008. "Secured lower bound, composition up, and minimal rights first for bankruptcy problems," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 925-932, September.
    18. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
    19. Krishna, Vijay & Serrano, Roberto, 1995. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(3), pages 259-272.
    20. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    21. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
    22. 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.
    23. Harless, Patrick, 2017. "Wary of the worst: Maximizing award guarantees when new claimants may arrive," Games and Economic Behavior, Elsevier, vol. 105(C), pages 316-328.
    24. 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.
    25. Chun, Youngsub, 1989. "A noncooperative justification for egalitarian surplus sharing," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 245-261, June.
    26. Serrano, Roberto & Vohra, Rajiv, 2002. "Bargaining and Bargaining Sets," Games and Economic Behavior, Elsevier, vol. 39(2), pages 292-308, May.
    27. Chang, Chih & Hu, Cheng-Cheng, 2008. "A non-cooperative interpretation of the f-just rules of bankruptcy problems," Games and Economic Behavior, Elsevier, vol. 63(1), pages 133-144, May.
    28. 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.
    29. Juan Moreno-Ternero, 2006. "Composition, Securement, and Concede-and-divide," Spanish Economic Review, Springer;Spanish Economic Association, vol. 8(3), pages 227-237, September.
    30. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    31. Serrano, Roberto, 1993. "Non-cooperative Implementation of the Nucleolus: The 3-Player Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(4), pages 345-357.
    32. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2018. "A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives," Games and Economic Behavior, Elsevier, vol. 109(C), pages 82-98.
    33. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
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    Cited by:

    1. Makoto Hagiwara & Shunsuke Hanato, 2021. "A strategic justification of the constrained equal awards rule through a procedurally fair multilateral bargaining game," Theory and Decision, Springer, vol. 90(2), pages 233-243, March.
    2. Roberto Serrano, 2020. "Sixty-Seven Years of the Nash Program: Time for Retirement?," Working Papers 2020-20, Brown University, Department of Economics.
    3. David Cerezo S'anchez, 2021. "JUBILEE: Secure Debt Relief and Forgiveness," Papers 2109.07267, arXiv.org.
    4. Juan D. Moreno-Ternero & Min-Hung Tsay & Chun-Hsien Yeh, 2021. "Strategic justifications of the TAL-family of rules for bankruptcy problems," Working Papers 21.02, Universidad Pablo de Olavide, Department of Economics.
    5. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.

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    More about this item

    Keywords

    Nash program; Strategic justification; Consistency; Lower bounds; Upper bounds; Talmud rule;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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