Power Measures and Solutions for Games Under Precedence Constraints
Encarnación Algaba (),
René Brink () and
Chris Dietz ()
Additional contact information
Encarnación Algaba: Escuela Superior de Ingenieros
René Brink: VU University
Chris Dietz: VU University
Journal of Optimization Theory and Applications, 2017, vol. 172, issue 3, No 14, 1008-1022
Abstract Games under precedence constraints model situations, where players in a cooperative transferable utility game belong to some hierarchical structure, which is represented by an acyclic digraph (partial order). In this paper, we introduce the class of precedence power solutions for games under precedence constraints. These solutions are obtained by allocating the dividends in the game proportional to some power measure for acyclic digraphs. We show that all these solutions satisfy the desirable axiom of irrelevant player independence, which establishes that the payoffs assigned to relevant players are not affected by the presence of irrelevant players. We axiomatize these precedence power solutions using irrelevant player independence and an axiom that uses a digraph power measure. We give special attention to the hierarchical solution, which applies the hierarchical measure. We argue how this solution is related to the known precedence Shapley value, which does not satisfy irrelevant player independence, and thus is not a precedence power solution. We also axiomatize the hierarchical measure as a digraph power measure.
Keywords: Game theory; Cooperative TU-game; Precedence constraint; Irrelevant player independence; Power measure; 91A12; 91A43 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-1057-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-016-1057-0
Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2
Access Statistics for this article
Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull
More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla ().