NDLI: On membership and marginal values

Content Provider	Springer Nature Link
Author	Kleinberg, rman L. Weiss, Jeffrey H.
Copyright Year	2013
Abstract	In Kleinberg and Weiss, Math Soc Sci 12:21–30 (1986b), the authors used the representation theory of the symmetric groups to characterize the space of linear and symmetric values. We call such values “membership” values, as a player’s payoff depends on the worths of the coalitions to which he belongs and not necessarily on his marginal contributions. This could mean that the player would get some share of $$v(N)$$ regardless of whether or not he makes a marginal contribution to the welfare of society. In this paper it is demonstrated that the set of (non-marginal) membership values include those that embody numerous widely held notions of fairness, such as partial “benefit equalization”, individual rationality and “greater rewards follow from greater contributions”, where one’s contributions are not measured marginally. We also present a very simple and revealing way of interpreting all values, including those having a marginal interpretation. Finally, we obtain a mapping which effectively embeds the space of marginal values in the space of all membership values.
Starting Page	357
Ending Page	373
Page Count	17
File Format	PDF
ISSN	00207276
Journal	International Journal of Game Theory
Volume Number	42
Issue Number	2
e-ISSN	14321270
Language	English
Publisher	Springer-Verlag
Publisher Date	2013-02-28
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Shapley value Membership value Egalitarian value Banzhaf value Fairness Equal allocation of non separable costs Economic Theory Game Theory, Economics, Social and Behav. Sciences Operations Research/Decision Theory Game Theory/Mathematical Methods
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Social Sciences Economics and Econometrics Statistics, Probability and Uncertainty

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