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Robustness of Intermediate Agreements and Bargaining Solutions

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Author Info
Nejat Anbarci ()
Ching-jen Sun ()

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Abstract

Most real-life bargaining is resolved gradually; two parties reach intermediate agreements without knowing the whole range of possibilities. These intermediate agreements serve as disagreement points in subsequent rounds. Cooperative bargaining solutions ignore these dynamics and can therefore yield accurate predictions only if they are robust to its specification. We identify robustness criteria which are satisfied by four of the best-known bargaining solutions, the Nash, Kalai-Smorodinsky, Proportional and Discrete Raiffa solutions. We show that the “robustness of intermediate agreements” plus additional well-known and plausible axioms, provide the first characterization of the Discrete Raiffa solution and novel axiomatizations of the other three solutions. Hence, we provide a unified framework for comparing these solutions’ bargaining theories.

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Paper provided by Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance in its series Economics Series with number 2009_14.

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Date of creation: 16 Sep 2009
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Handle: RePEc:dkn:econwp:eco_2009_14

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Related research
Keywords: Nash’s bargaining problem; robustness; intermediate agreements; the Discrete Raiffa solution; the Nash solution; the Kalai-Smorodinsky solution; Proportional solutions.;

Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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  1. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May. [Downloadable!] (restricted)
  2. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January. [Downloadable!] (restricted)
  3. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106. [Downloadable!] (restricted)
  4. Anbarci, Nejat & Yi, Gyoseob, 1992. "A meta-allocation mechanism in cooperative bargaining," Economics Letters, Elsevier, vol. 38(2), pages 175-179, February. [Downloadable!] (restricted)
  5. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April. [Downloadable!] (restricted)
  6. Anbarci, Nejat & Skaperdas, Stergios & Syropoulos, Constantinos, 2002. "Comparing Bargaining Solutions in the Shadow of Conflict: How Norms against Threats Can Have Real Effects," Journal of Economic Theory, Elsevier, vol. 106(1), pages 1-16, September. [Downloadable!] (restricted)
    Other versions:
  7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  8. Damme, Eric van, 1986. "The Nash bargaining solution is optimal," Journal of Economic Theory, Elsevier, vol. 38(1), pages 78-100, February. [Downloadable!] (restricted)
  9. Nejat Anbarci, 1995. "Reference Functions and Balanced Concessions in Bargaining," Canadian Journal of Economics, Canadian Economics Association, vol. 28(3), pages 675-82, August. [Downloadable!] (restricted)
  10. Bigelow, John Payne & Anbarci, Nejat, 1993. "Non-dictatorial, Pareto-monotonic, cooperative bargaining : An impossibility theorem," European Journal of Political Economy, Elsevier, vol. 9(4), pages 551-558, November. [Downloadable!] (restricted)
  11. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, vol. 56(1), pages 142-159, February. [Downloadable!] (restricted)
  12. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-77, May. [Downloadable!] (restricted)
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  14. Moulin, H., 1984. "Implementing the Kalai-Smorodinsky bargaining solution," Journal of Economic Theory, Elsevier, vol. 33(1), pages 32-45, June. [Downloadable!] (restricted)
  15. Anbarci, Nejat, 1993. "Noncooperative Foundations of the Area Monotonic Solutions," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 245-58, February. [Downloadable!] (restricted)
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    Other versions:
  18. Thomson, William, 1987. "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, Elsevier, vol. 42(1), pages 50-58, June. [Downloadable!] (restricted)
  19. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October. [Downloadable!] (restricted)
    Other versions:
  20. Gur Huberman, 2001. "Contagious Speculation and a Cure for Cancer: A Nonevent that Made Stock Prices Soar," Journal of Finance, American Finance Association, vol. 56(1), pages 387-396, 02. [Downloadable!] (restricted)
  21. Anbarci, Nejat & Bigelow, John P., 1994. "The area monotonic solution to the cooperative bargaining problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 133-142, October. [Downloadable!] (restricted)
  22. Geoffroy Clippel, 2007. "An axiomatization of the Nash bargaining solution," Social Choice and Welfare, Springer, vol. 29(2), pages 201-210, September. [Downloadable!] (restricted)
    Other versions:
  23. Chun, Youngsub & Thomson, William, 1990. "Bargaining with Uncertain Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 951-59, July. [Downloadable!] (restricted)
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