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Relative Responsiveness of Bargaining Solutions to Changes in Status-quo Payoffs

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  • Nejat Anbarci

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Abstract

It is a well-known fact that several prominent bargaining solutions are responsive to changes in status-quo (i.e., disagreement or fallback) payoffs. When an agent’s status-quo payoff increases, his solution payoff either stays the same or increases. A fully general result for these solutions’ status-quo point ranking is impossible to establish. In this paper, using an important class of bargaining problems, a ranking of the relative status-quo point responsiveness of prominent bargaining solutions is obtained. Using the Constant Elasticity of Substitution class of bargaining problems, regardless of the concavity of the Pareto frontier and the level of increase in one’s status-quo payoff, we find the equal gains solution is the most responsive with respect to changes in status-quo payoffs, followed by the Nash solution. The equal sacrifice solutions is the least responsive, followed by the Kalai/Smorodinsky solution. Copyright International Atlantic Economic Society 2008

Suggested Citation

  • Nejat Anbarci, 2008. "Relative Responsiveness of Bargaining Solutions to Changes in Status-quo Payoffs," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 36(3), pages 293-299, September.
  • Handle: RePEc:kap:atlecj:v:36:y:2008:i:3:p:293-299
    DOI: 10.1007/s11293-008-9135-9
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    File URL: http://hdl.handle.net/10.1007/s11293-008-9135-9
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    References listed on IDEAS

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    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    3. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-777, May.
    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.
    7. Nejat Anbarci, 1997. "Noncooperative foundations for the kalai-smorodinsky and equal sacrifice solutions via prominence structures," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 25(4), pages 403-411, December.
    8. 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.
    9. Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
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    More about this item

    Keywords

    Status-quo payoffs; The Nash solution; The Kalai/Smorodinsky solution; The egalitarian solution; The equal sacrifice solution; The equal gains solution; C78; D70;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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