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A note on the Sobolev consistency of linear symmetric values

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  • Norman Kleinberg

Abstract

In van den Brink et al. (Soc Choice Welf 40:693–714, 2013 ) it is demonstrated that every $$\alpha $$ α -egalitarian value (Joosten in Dynamics, equilibria and values dissertation, Maastricht University, Maastricht, 1996 ) is consistent with respect to the well-known Sobolev reduced game function. However, the authors did not consider the question of whether or not these were the only Sobolev-consistent values. In this note we delineate, in the context of cooperative games with transferable utility and linear, symmetric and efficient values, the entire set of solutions that are consistent with respect to the Sobolev function. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Norman Kleinberg, 2015. "A note on the Sobolev consistency of linear symmetric values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 765-779, April.
    • Handle: RePEc:spr:sochwe:v:44:y:2015:i:4:p:765-779
    DOI: 10.1007/s00355-014-0859-y
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    References listed on IDEAS

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    1. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    2. Kleinberg, Norman L. & Weiss, Jeffrey H., 1986. "Weak values, the core, and new axioms for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 12(1), pages 21-30, August.
    3. Theo Driessen, 2010. "Associated consistency and values for TU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 467-482, July.
    4. René Brink & Yukihiko Funaki & Yuan Ju, 2013. "Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 693-714, March.
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    Cited by:

    1. Norman L. Kleinberg, 2018. "A note on associated consistency and linear, symmetric values," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 913-925, September.

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