Annals of Operations Research

, Volume 243, Issue 1, pp 179–198

An Owen-type value for games with two-level communication structure

  • René van den Brink
  • Anna Khmelnitskaya
  • Gerard van der Laan
Article

DOI: 10.1007/s10479-015-1808-6

Cite this article as:
van den Brink, R., Khmelnitskaya, A. & van der Laan, G. Ann Oper Res (2016) 243: 179. doi:10.1007/s10479-015-1808-6

Abstract

We introduce an Owen-type value for games with two-level communication structure, which is a structure where the players are partitioned into a coalition structure such that there exists restricted communication between as well as within the a priori unions of the coalition structure. Both types of communication restrictions are modeled by an undirected communication graph. We provide an axiomatic characterization of the new value using an efficiency, two types of fairness (one for each level of the communication structure), and a new type of axiom, called fair distribution of the surplus within unions, which compares the effect of replacing a union in the coalition structure by one of its maximal connected components on the payoffs of these components. The relevance of the new value is illustrated by an example. We also show that for particular two-level communication structures the Owen value and the Aumann–Drèze value for games with coalition structure, the Myerson value for communication graph games, and the equal surplus division solution appear as special cases of this new value.

Keywords

TU game Coalition structure Communication graph Owen value  Myerson value 

JEL Classification

C71 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • René van den Brink
    • 1
  • Anna Khmelnitskaya
    • 2
  • Gerard van der Laan
    • 1
  1. 1.Department of Econometrics and Tinbergen InstituteVU UniversityAmsterdamThe Netherlands
  2. 2.Faculty of Applied MathematicsSaint-Petersburg State UniversityPetergof, Saint PetersburgRussia