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Twofold Optimality of the Relative Utilitarian Bargaining Solution

  • Pivato, Marcus

Given a bargaining problem, the `relative utilitarian' (RU) solution maximizes the sum total of the bargainer's utilities, after having first renormalized each utility function to range from zero to one. We show that RU is `optimal' in two very different senses. First, RU is the maximal element (over the set of all bargaining solutions) under any partial ordering which satisfies certain axioms of fairness and consistency; this result is closely analogous to the result of Segal (2000). Second, RU offers each person the maximum expected utility amongst all rescaling-invariant solutions, when it is applied to a random sequence of future bargaining problems which are generated using a certain class of distributions; this is somewhat reminiscent of the results of Harsanyi (1953) and Karni (1998).

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File URL: https://mpra.ub.uni-muenchen.de/2637/1/MPRA_paper_2637.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 2637.

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Date of creation: 09 Apr 2007
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Handle: RePEc:pra:mprapa:2637
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  1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  2. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
  3. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  4. Uzi Segal, 2000. "Let's Agree That All Dictatorships Are Equally Bad," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 569-589, June.
  5. Edi Karni, 1998. "Impartiality: Definition and Representation," Econometrica, Econometric Society, vol. 66(6), pages 1405-1416, November.
  6. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  7. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer, vol. 15(4), pages 521-542.
  8. Eric Maskin, 1978. "A Theorem on Utilitarianism," Review of Economic Studies, Oxford University Press, vol. 45(1), pages 93-96.
  9. John C. Harsanyi, 1953. "Cardinal Utility in Welfare Economics and in the Theory of Risk-taking," Journal of Political Economy, University of Chicago Press, vol. 61, pages 434.
  10. Edi Karni & John A. Weymark, 1998. "An informationally parsimonious impartial observer theorem," Social Choice and Welfare, Springer, vol. 15(3), pages 321-332.
  11. Yew-Kwang Ng, 1975. "Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions," Review of Economic Studies, Oxford University Press, vol. 42(4), pages 545-569.
  12. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, 1.
  13. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  14. Edi Karni, 2003. "Impartiality and interpersonal comparisons of variations in well-being," Social Choice and Welfare, Springer, vol. 21(1), pages 95-111, 08.
  15. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
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