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

  • Nejat Anbarci

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    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

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    File URL: http://hdl.handle.net/10.1007/s11293-008-9135-9
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    Article provided by International Atlantic Economic Society in its journal Atlantic Economic Journal.

    Volume (Year): 36 (2008)
    Issue (Month): 3 (September)
    Pages: 293-299

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    Handle: RePEc:kap:atlecj:v:36:y:2008:i:3:p:293-299
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    1. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
    3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-77, May.
    7. Nejat Anbarci, 1997. "Noncooperative foundations for the kalai-smorodinsky and equal sacrifice solutions via prominence structures," Atlantic Economic Journal, International Atlantic Economic Society, vol. 25(4), pages 403-411, December.
    8. 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.
    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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