Core Stability in Chain-Component Additive Games

CentER Discussion Paper No. 2004-101

20 Pages Posted: 15 Dec 2004

See all articles by Bas van Velzen

Bas van Velzen

affiliation not provided to SSRN

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Tamas Solymosi

Corvinus University of Budapest

Date Written: October 2004

Abstract

Chain-component additive games are graph-restricted superadditive games, where an exogenously given line-graph determines the cooperative possibilities of the players. These games can model various multi-agent decision situations, such as strictly hierarchical organisations or sequencing/scheduling related problems, where an order of the agents is fixed by some external factor, and with respect to this order only consecutive coalitions can generate added value. In this paper we characterise core stability of chain-component additive games in terms of polynomial many linear inequalities and equalities that arise from the combinatorial structure of the game. Furthermore we show that core stability is equivalent to essential extendibility. We also obtain that largeness of the core as well as extendibility and exactness of the game are equivalent properties which are all sufficient for core stability. Moreover, we also characterise these properties in terms of linear inequalities.

Keywords: Core stability, graph-restricted games, large core, exact game

JEL Classification: C71

Suggested Citation

Velzen, Bas van and Hamers, Herbert and Solymosi, Tamas, Core Stability in Chain-Component Additive Games (October 2004). CentER Discussion Paper No. 2004-101. Available at SSRN: https://ssrn.com/abstract=627341 or http://dx.doi.org/10.2139/ssrn.627341

Bas van Velzen (Contact Author)

affiliation not provided to SSRN ( email )

No Address Available

Herbert Hamers

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Tamas Solymosi

Corvinus University of Budapest ( email )

1828 Budapest
Pf. 489
Hungary
36-1-217 4505 (Phone)

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