Solidarity induced by group contributions: the MI $$^k$$ k -value for transferable utility games

Surajit Borkotokey (), Loyimee Gogoi (), Dhrubajit Choudhury () and Rajnish Kumar ()
Additional contact information
Loyimee Gogoi: Northwestern Polytechnical University
Dhrubajit Choudhury: Dibrugarh University
Rajnish Kumar: Queen’s University

Operational Research, 2022, vol. 22, issue 2, No 15, 1267-1290

Abstract: Abstract The most popular values in cooperative games with transferable utilities are perhaps the Shapley and the Shapley like values which are based on the notion of players’ marginal productivity. The equal division rule on the other hand, is based on egalitarianism where resource is equally divided among players, no matter how productive they are. However none of these values explicitly discuss players’ multilateral interactions with peers in deciding to form coalitions and generate worths. In this paper we study the effect of multilateral interactions of a player that accounts for her contributions with her peers not only at an individual level but also on a group level. Based on this idea, we propose a value called the MI $$^k$$ k -value and characterize it by the axioms of linearity, anonymity, efficiency and a new axiom: the axiom of MN $$^k$$ k -player. An MN $$^k$$ k -player is one whose average marginal contribution due to her multilateral interactions upto level k is zero and can be seen as a generalization of the standard null player axiom of the Shapley value. We have shown that the MI $$^k$$ k -value on a variable player set is asymptotically close to the equal division rule. Thus our value realizes solidarity among players by incorporating both their individual and group contributions.

Keywords: Group contributions; Multilateral Interactions; MN $$^{k}$$ k -player; MI $$^{k}$$ k -value; 91A12 (search for similar items in EconPapers)
JEL-codes: C71 D63 D81 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12351-020-00584-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:operea:v:22:y:2022:i:2:d:10.1007_s12351-020-00584-4

Ordering information: This journal article can be ordered from
https://www.springer ... search/journal/12351

DOI: 10.1007/s12351-020-00584-4

Access Statistics for this article

Operational Research is currently edited by Nikolaos F. Matsatsinis, John Psarras and Constantin Zopounidis

More articles in Operational Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().