Solution concepts for games with general coalitional structure

G.A. Koshevoy, A.J.J. Talman

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We introduce a theory of marginal values and their core stability for cooperative games with transferable utility and arbitrary set systems representing the set of feasible coalitions. The theory is based on the notion of strictly nested sets in a set system. For each maximal strictly nested set, we define a unique marginal contribution vector. Using these marginal contribution vectors several solutions concepts are introduced.

The gravity center or GC-solution of a game is defined as the average of the marginal vectors over all maximal strictly nested sets. For union stable set systems, buildings sets, the GC-solution differs from Myerson-type solutions. The half-space or HS-solution is defined as the average of the marginal vectors over the class of so-called half-space nested sets and is appropriate for example when feasible coalitions represent social networks. The normal tree or NT-solution is defined as the average of the marginal vectors over all so-called NT-nested sets and is appropriate when feasibility of a coalition is based on bilateral communication between players. For graphical building sets, the NT-solution is equal to the average tree solution. We also study core stability of the solutions and show that the conditions under which the HS- and NT-solutions belong to the core are weaker than conditions under which the GC-solution is stable.

For a more general set system, there exists a unique minimal building set containing the set system, its building covering. As solutions for games on an arbitrary set system of feasible coalitions we propose to take the solutions for its building covering with respect to the M-extension of the characteristic function of the game.
Original languageEnglish
Pages (from-to)19-30
JournalMathematical Social Sciences
Volume68
DOIs
Publication statusPublished - 2014

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Solution Concepts
Set Systems
Game
coalition
Coalitions
Strictly
Half-space
Covering
Solution concepts
building
social network
Stable Set
Cooperative Game
Arbitrary
Characteristic Function
Social Networks
communication
Gravity
Union
Values

Cite this

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Solution concepts for games with general coalitional structure. / Koshevoy, G.A.; Talman, A.J.J.

In: Mathematical Social Sciences, Vol. 68, 2014, p. 19-30.

Research output: Contribution to journalArticleScientificpeer-review

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