The equal-surplus Shapley value for chance-constrained games on finite sample spaces

Donald Nganmegni Njoya (), Issofa Moyouwou () and Nicolas Gabriel Andjiga ()
Additional contact information
Donald Nganmegni Njoya: University of Yaounde I
Issofa Moyouwou: University of Yaounde I
Nicolas Gabriel Andjiga: University of Yaounde I

Mathematical Methods of Operations Research, 2021, vol. 93, issue 3, No 2, 463-499

Abstract: Abstract Many interactions from linear production problems, financial markets, or sequencing problems are modeled by cooperative games where payoffs to a coalition of players is a random variable. For this class of cooperative games, we introduce a two-stage value as an ex-ante agreement among players. Players are first promised their prior Shapley shares which are exactly their respective shares by the Shapley value of the expectation game. The final payoff vector is obtained by equally re-allocating the surplus when a realization of the random payoff of the grand coalition is observed. In support of the tractability of the newly introduced value called equal-surplus Shapley value, we provide a simple and compact formula. Depending on which probability distributions over the sample spaces are admissible, we present several characterization results of the equal-surplus Shapley value. This is achieved by using some classical axioms together with some other appealing axioms such as the independence of local duplication which simply requires that individual shares in a game remain unchanged when only certain events are duplicated in the sample space of a coalition without altering the probability of observing the others.

Keywords: Game theory; Random coalitional payoffs; Equal surplus; Finite sample spaces (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00186-021-00738-w 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:mathme:v:93:y:2021:i:3:d:10.1007_s00186-021-00738-w

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-021-00738-w

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().