Cooperative game theory

Cooperative game theory studies which coalitions can form and how their joint gains can be allocated. It models cooperation through coalition values or feasible payoff sets, rather than requiring every player to act independently.

Coalition: A group of players that can coordinate their actions in a strategic setting. Coalitions are the units whose joint capabilities and gains the theory analyzes.
Shapley value: A payoff rule that assigns each player its average marginal contribution across all joining orders. It gives a unique allocation satisfying efficiency, symmetry, null-player, and additivity axioms.
Cost allocation: The assignment of a joint project's costs among the participants who benefit from it. Cooperative solution concepts can guide fair and stable divisions of shared expenses.
John von Neumann: A mathematician who helped establish modern game theory and introduced the minimax theorem with Oskar Morgenstern. His work with Morgenstern supplied the field's mathematical foundations.
Non-cooperative game theory: Game theory that models players' strategies, incentives, and outcomes without assuming binding cooperation. It represents interaction through individual strategic choices rather than coalition values.
Characteristic function: A function assigning each coalition the value it can obtain independently of other players. It encodes coalition-making possibilities in the transferable-utility model.
Nucleolus: A solution that lexicographically minimizes coalitions' largest excesses over their allocated payoffs. It selects a compromise by reducing the most dissatisfied coalition first.
Voting power: A measure of how much a participant can influence outcomes in a voting system. Coalitional models capture how blocs of voters affect collective decisions.
Oskar Morgenstern: An economist who coauthored the foundational book Theory of Games and Economic Behavior with John von Neumann. The book developed the distinction between cooperative and noncooperative game models.
Strategic-form game: A game represented by players, strategy sets, and payoffs for every strategy profile. It is a standard non-cooperative representation, unlike a coalition-value description.

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