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A Noncooperative Support for Equal Division in Estate Division Problems

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  • Itai Ashlagi

    ()
    (Harvard Business School, Negotiation, Organizations & Markets Unit)

  • Emin Karagozoglu

    ()
    (Department of Economics, Maastricht University)

  • Bettina Klaus

    ()
    (Harvard Business School, Negotiation, Organizations & Markets Unit)

Abstract

We consider estate division problems, a generalization of bankruptcy problems. We show that in a direct revelation claim game, if the underlying division rule satisfies efficiency, equal treatment of equals, and weak order preservation, then all (pure strategy) Nash equilibria induce equal division. Next, we consider division rules satisfying efficiency, equal treatment of equals, and claims monotonicity. For claim games with at most three agents, again all Nash equilibria induce equal division. Surprisingly, this result does not extend to claim games with more than three agents. However, if nonbossiness is added, then equal division is restored.

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Bibliographic Info

Paper provided by Harvard Business School in its series Harvard Business School Working Papers with number 09-069.

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Length: 15 pages
Date of creation: Nov 2008
Date of revision:
Handle: RePEc:hbs:wpaper:09-069

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Keywords: Bankruptcy/estate division problems; claims monotonicity; direct revelation claim game; equal division; equal treatment of equals; Nash equilibria; nonbossiness; (weak) order preservation.;

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  1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, Econometric Society, vol. 21(1), pages 128-140, April.
  2. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 48(4), pages 587-97, October.
  3. Itai Ashlagi & Emin Karagozoglu & Bettina Klaus, 2008. "A Noncooperative Support for Equal Division in Estate Division Problems," Harvard Business School Working Papers, Harvard Business School 09-069, Harvard Business School.
  4. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(3), pages 249-297, July.
  5. Simon Gächter & Arno Riedl, 2005. "Moral Property Rights in Bargaining with Infeasible Claims," Management Science, INFORMS, INFORMS, vol. 51(2), pages 249-263, February.
  6. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer, Springer, vol. 14(1), pages 1-15, March.
  7. Allan M. Feldman & Jeonghyun Kim, 2005. "The Hand Rule and United States v. Carroll Towing Co. Reconsidered," American Law and Economics Review, Oxford University Press, Oxford University Press, vol. 7(2), pages 523-543.
  8. Simon Gaechter & Arno Riedl, 2002. "Moral Property Rights in Bargaining," CESifo Working Paper Series 697, CESifo Group Munich.
  9. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, Elsevier, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357 Elsevier.
  10. Chun, Youngsub, 1989. "A noncooperative justification for egalitarian surplus sharing," Mathematical Social Sciences, Elsevier, Elsevier, vol. 17(3), pages 245-261, June.
  11. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 195-213, August.
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Cited by:
  1. Anita Gantner & Kristian Horn & Rudolf Kerschbamer, 2013. "Fair Division in Unanimity Bargaining with Subjective Claims," Working Papers, Faculty of Economics and Statistics, University of Innsbruck 2013-31, Faculty of Economics and Statistics, University of Innsbruck.
  2. Itai Ashlagi & Emin Karagozoglu & Bettina Klaus, 2008. "A Noncooperative Support for Equal Division in Estate Division Problems," Harvard Business School Working Papers, Harvard Business School 09-069, Harvard Business School.
  3. William Thomson, 2013. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update," RCER Working Papers 578, University of Rochester - Center for Economic Research (RCER).
  4. Karagözoğlu, Emin & Keskin, Kerim & Sağlam, Çağrı, 2013. "A minimally altruistic refinement of Nash equilibrium," Mathematical Social Sciences, Elsevier, Elsevier, vol. 66(3), pages 422-430.
  5. Esat Cetemen & Emin Karagözoğlu, 2014. "Implementing equal division with an ultimatum threat," Theory and Decision, Springer, Springer, vol. 77(2), pages 223-236, August.

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