Core stability of flow games

Authors:
Xiaoxun Sun;Qizhi Fang
Affiliations:
Department of Mathematics, Ocean University of China, Qingdao, P.R. China;Department of Mathematics, Ocean University of China, Qingdao, P.R. China
Venue:
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Year:
2005

Citing 3
Cited 4

On the complexity of cooperative solution concepts

Mathematics of Operations Research
Algorithmic Aspects of the Core of Combinatorial Optimization Games

Mathematics of Operations Research
Core stability of minimum coloring games

WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science

Power in threshold network flow games

Autonomous Agents and Multi-Agent Systems
Restricted Core Stability of Flow Games

WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Core stability of vertex cover games

WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Algorithms for core stability, core largeness, exactness, and extendability of flow games

COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study the problem of core stability for flow games, introduced by Kalai and Zemel (1982), which arises from the profit distribution problem related to the maximum flow in networks. Based on the characterization of dummy arc (i.e., the arc which satisfies that deleting it does not change the value of maximum flow in the network), we prove that the flow game defined on a simple network has the stable core if and only if there is no dummy arc in the network. We also show that the core largeness, the extendability and the exactness of flow games are equivalent conditions, which strictly imply the stability of the core.