Coalition (game theory, $S\subseteq N$)

A coalition is a subset of the players in a transferable utility game, considered as a group that can act together. The game assigns it value $v(S)$. The core of a cooperative game constrains the total payoff assigned to every coalition, while a marginal contribution measures the value gained by adding one player.

The excess measures a coalition's complaint against an allocation: a positive excess means its own attainable value exceeds its assigned total. The core of a cooperative game requires every excess to be nonpositive at an efficient allocation. The nucleolus lexicographically minimizes the decreasingly sorted excess vector over imputations.