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Evolution of Division Rules

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  • Birendra K. Rai

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Abstract

Several division rules have been proposed in the literature regarding how an arbiter should divide a bankrupt estate. Different rules satisfy different sets of axioms, but all rules satisfy claims boundedness which requires that no contributor be given more than her initial contribution. This paper takes two non-cooperative bargaining games - the contracting game (Young, 1998a), and the Nash demand game, and adds the axiom of claims boundedness to the rules of these games. Outcomes prescribed by all the division rules are strict Nash equilibria in the one-shot version of both these augmented games. We show that the division suggested by the truncated claims proportional rule is the unique long run outcome if we embed the augmented contracting game in Young’s (1993b) evolutionary bargaining model. With the augmented Nash demand game as the underlying bargaining game, the long run outcome is the division prescribed by the constrained equal awards rule.

Suggested Citation

  • Birendra K. Rai, 2006. "Evolution of Division Rules," Papers on Strategic Interaction 2006-27, Max Planck Institute of Economics, Strategic Interaction Group.
  • Handle: RePEc:esi:discus:2006-27
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    References listed on IDEAS

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    1. Michihiro, Kandori & Rob, Rafael, 1998. "Bandwagon Effects and Long Run Technology Choice," Games and Economic Behavior, Elsevier, vol. 22(1), pages 30-60, January.
    2. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    3. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, January.
    4. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    5. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    6. Ellingsen, Tore & Robles, Jack, 2002. "Does Evolution Solve the Hold-Up Problem?," Games and Economic Behavior, Elsevier, vol. 39(1), pages 28-53, April.
    7. 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.
    8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    9. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    10. Simon Gächter & Arno Riedl, 2006. "Dividing Justly in Bargaining Problems with Claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 571-594, December.
    11. H. Peyton Young, 1998. "Conventional Contracts," Review of Economic Studies, Oxford University Press, vol. 65(4), pages 773-792.
    12. Troger, Thomas, 2002. "Why Sunk Costs Matter for Bargaining Outcomes: An Evolutionary Approach," Journal of Economic Theory, Elsevier, vol. 102(2), pages 375-402, February.
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    More about this item

    Keywords

    fair division; stochastic stability;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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