The Cost of Stability in Coalitional Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Monotone cooperative games and their threshold versions
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
On the stability of an Optimal Coalition Structure
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Minimal subsidies in expense sharing games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
The least-core of threshold network flow games
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Rip-off: playing the cooperative negotiation game
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
Graph-based coalitional games: an analysis via characteristics
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Agent failures in totally balanced games and convex games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Proof systems and transformation games
Annals of Mathematics and Artificial Intelligence
Computing cooperative solution concepts in coalitional skill games
Artificial Intelligence
Sharing rewards in cooperative connectivity games
Journal of Artificial Intelligence Research
Hi-index | 0.00 |
One key question in cooperative game theory is that of coalitional stability. A coalition in such games is stable when no subset of the agents in it has a rational incentive to leave the coalition. Finding a division of the gains of the coalition (an imputation) lies at the heart of many cooperative game theory solution concepts, the most prominent of which is the core. However, some coalitional games have empty cores, and any imputation in such a game is unstable. We investigate the possibility of stabilizing the coalitional structure using external payments. In this case, a supplemental payment is offered to the grand coalition by an external party which is interested in having the members of the coalition work together. The sum of this payment plus the gains of the coalition, called the coalition's "adjusted gains", may be divided among the members of the coalition in a stable manner. We call a division of the adjusted gains a super-imputation, and define the cost of stability (CoS) as the minimal sum of payments that stabilizes the coalition. We examine the cost of stability in weighted voting games, where each agent has a weight, and a coalition is successful if the sum of its weights exceeds a given threshold. Such games offer a simple model of decision making in political bodies, and of cooperation in multiagent settings. We show that it is coNP-complete to test whether a super-imputation is stable, but show that if either the weights or payments of agents are bounded then there exists a polynomial algorithm for this problem. We provide a polynomial approximation algorithm for computing the cost of stability.