 Characteristic function of a coalitional game

The characteristic function assigns every coalition its total attainable transferable payoff, with $v(\varnothing )=0$. It determines the efficiency condition of an imputation and all constraints of the core of a cooperative game. For the glove game, $v(S)=\omega \min (|S\cap L|,|S\cap R|)$; for miners requiring $r$ people to carry one lump, $v(S)=\lfloor |S|/r\rfloor$. This game-theoretic function is distinct from the characteristic function of a probability distribution.