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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.

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Bibliographic Info

Paper provided by Max Planck Institute of Economics, Strategic Interaction Group in its series Papers on Strategic Interaction with number 2006-27.

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Length: 21 pages
Date of creation: Oct 2006
Date of revision:
Handle: RePEc:esi:discus:2006-27

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Keywords: fair division; stochastic stability;

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  1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 43(3), pages 513-18, May.
  2. Michihiro Kandori & Rafael Rob, 1997. "Bandwagon effects and long run technology choice," Levine's Working Paper Archive 1265, David K. Levine.
  3. 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.
  4. Ellingsen, Tore & Robles, Jack, 2002. "Does Evolution Solve the Hold-Up Problem?," Games and Economic Behavior, Elsevier, vol. 39(1), pages 28-53, April.
  5. Simon G�chter & Arno Riedl, 2004. "Dividing justly in Bargaining Problems with Claims," Tinbergen Institute Discussion Papers 04-044/1, Tinbergen Institute.
  6. Young, H Peyton, 1998. "Conventional Contracts," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(4), pages 773-92, October.
  7. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
  8. J. Bergin & B. Lipman, 2010. "Evolution with State-Dependent Mutations," Levine's Working Paper Archive 486, David K. Levine.
  9. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
  10. 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.
  11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
  12. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
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