Coalition Formation
Study of which coalitions form and how they share surplus.
Definition
Partition function games assign value to each coalition within a coalition structure (partition).
Hedonic games assign each player a preference over coalitions containing them and study stable partitions.
Intuition
Beyond "everyone cooperates", who teams up with whom and why?
Stability, fairness, and efficiency of partitions are all considered.
Worked example
In hedonic matching (roommate problem), no-blocking partitions may not exist.
In political coalitions, the Banzhaf and Shapley-Shubik power indices measure pivotal influence.
The math
Core-stability, Nash-stability, and individual stability each capture different robustness concepts for partitions.
Even in simple hedonic games, computing stable partitions can be NP-hard.
Where it is used
Political alliances, R&D consortia, group formation in social networks, and team formation in distributed computing.
Connects to matching theory and hedonic preferences.
More in Game theory
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