Consolidating Marginalism and Egalitarianism: A New Value for Transferable Utility Games

20 Pages Posted: 13 Nov 2020

See all articles by Surajit Borkotokey

Surajit Borkotokey

Dibrugarh University

Dhrubajit Choudhury

Dibrugarh University

Rajnish Kumar

Queen's University Management School

Sudipta Sarangi

Virginia Polytechnic Institute & State University

Date Written: November 13, 2020

Abstract

In cooperative games with transferable utilities, the Shapley value is an extreme case of marginalism while the Equal Division rule is an extreme case of egalitarianism. The Shapley value does not assign anything to the non-productive players and the Equal Division rule does not concern itself to the relative efficiency of the players in generating a resource. However, in real life situations neither of them is a good fit for the fair distribution of resources as the society is neither devoid of solidarity nor it can be indifferent to rewarding the relatively more productive players. Thus a trade-off between these two extreme cases has caught attention from many researchers. In this paper, we obtain a new value for cooperative games with transferable utilities that adopts egalitarianism in smaller coalitions on one hand and on the other hand takes care of the players' marginal productivity in sufficiently large coalitions. Our value is identical with the Shapley value on one extreme and the Equal Division rule on the other extreme. We provide four characterizations of the value using variants of standard axioms in the literature. We also provide a mechanism that implements our value in sub-game perfect Nash equilibrium.

Keywords: Shapley value, Equal Division rule, Solidarity, Egalitarian Shapley value

JEL Classification: C71, D60

Suggested Citation

Borkotokey, Surajit and Choudhury, Dhrubajit and Kumar, Rajnish and Sarangi, Sudipta, Consolidating Marginalism and Egalitarianism: A New Value for Transferable Utility Games (November 13, 2020). QMS Research Paper 2020/12, Available at SSRN: https://ssrn.com/abstract=3729927 or http://dx.doi.org/10.2139/ssrn.3729927

Surajit Borkotokey

Dibrugarh University ( email )

Dibrugarh - 786 004
Assam, IN Assam 786004
India

Dhrubajit Choudhury

Dibrugarh University ( email )

Dibrugarh - 786 004
Assam, IN Assam 786004
India

Rajnish Kumar (Contact Author)

Queen's University Management School ( email )

25 University Square
Belfast, Northern Ireland BT7 1NN
Northern Ireland

Sudipta Sarangi

Virginia Polytechnic Institute & State University ( email )

250 Drillfield Drive
Blacksburg, VA 24061
United States

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