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Randomized dictatorship and the Kalai–Smorodinsky bargaining solution

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  • Shiran Rachmilevitch

Abstract

“Randomized dictatorship,” one of the simplest ways to solve bargaining situations, works as follows: a fair coin toss determines the “dictator”—the player to be given his first-best payoff. The two major bargaining solutions, that of Nash (Econometrica 18:155–162, 1950 ) and that of Kalai and Smorodinsky (Econometrica, 43:513–518, 1975 ), Pareto-dominate this process (in the ex ante sense). However, whereas the existing literature offers axiomatizations of the Nash solution in which this ex ante domination plays a central role (Moulin, Le choix social utilitariste, Ecole Polytechnique Discussion Paper, 1983 ; de Clippel, Social Choice and Welfare, 29:201–210, 2007 ), it does not provide an analogous result for Kalai–Smorodinsky. This paper fills in this gap: a characterization of the latter is obtained by combining the aforementioned domination with three additional axioms: Pareto optimality, individual monotonicity, and a weakened version of the Perles–Maschler (International Journal of Game Theory, 10:163–193, 1981 ) super additivity axiom. Copyright Springer Science+Business Media New York 2014

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  • Shiran Rachmilevitch, 2014. "Randomized dictatorship and the Kalai–Smorodinsky bargaining solution," Theory and Decision, Springer, vol. 76(2), pages 173-177, February.
    • Handle: RePEc:kap:theord:v:76:y:2014:i:2:p:173-177
    DOI: 10.1007/s11238-013-9367-2
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    References listed on IDEAS

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    1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    2. Geoffroy Clippel, 2007. "An axiomatization of the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 201-210, September.
    3. Myerson, Roger B, 1981. "Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems," Econometrica, Econometric Society, vol. 49(4), pages 883-897, June.
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    5. Nejat Anbarci, 1998. "Simple Characterizations of the Nash and Kalai/smorodinsky Solutions," Theory and Decision, Springer, vol. 45(3), pages 255-261, December.
    6. 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.
    7. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
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    Cited by:

    1. Karos, Dominik & Rachmilevitch, Shiran, 2018. "The Midpoint-Constrained Egalitarian Bargaining Solution," Research Memorandum 007, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Karos, Dominik & Rachmilevitch, Shiran, 2019. "The midpoint-constrained egalitarian bargaining solution," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 107-112.

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