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From Bargaining Solutions to Claims Rules: A Proportional Approach

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  • Giménez-Gómez, José-Manuel

    ()
    (Universitat Rovira i Virgili)

  • Osorio, Antonio

    ()
    (Universitat Rovira i Virgili)

  • Peris, Josep Enric

    ()
    (Universitat d'Alacant)

Abstract

Is it important to negotiate on proportions rather than on numbers? To answer this question, we analyze the behavior of well-known bargaining solutions and the claims rules they induce when they are applied to a "proportionally transformed" bargaining set SP so-called bargaining-in-proportions set. The idea of applying bargaining solutions to claims problems was already developed in Dagan and Volij (1993). They apply the bargaining solutions over a bargaining set that is the one de ned by the claims and the endowment. A comparison among our results and theirs is provided.

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Paper provided by Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica in its series QM&ET Working Papers with number 13-2.

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Length: 21 pages
Date of creation: 27 May 2013
Date of revision:
Handle: RePEc:ris:qmetal:2013_002

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Keywords: Bargaining problem; Claims problem; Proportional Constrained Equal Awards; Constrained Equal Losses; Nash bargaining solution;

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  1. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
  2. Volij, Oscar & Dagan, Nir, 1993. "The Bankruptcy Problem: A Cooperative Bargaining Approach," Staff General Research Papers 10571, Iowa State University, Department of Economics.
  3. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284 Elsevier.
  4. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
  5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  6. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  8. 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.
  9. 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.
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