= Shapley value denominator in a simple game
{c}
{title2=$n!\phi_i(v)\in\mathbb Z$}
In an $n$-player <simple cooperative game>, every <marginal contribution> along a player <permutation> is zero or one. The <Shapley value> is its average over the $n!$ equally likely <permutations>. Thus $n!\phi_i(v)$ counts the orders in which player $i$ changes a losing <coalition> into a winning one and is an <integer>. In lowest terms, the coordinate's denominator divides $n!$. This is a necessary constraint on a proposed <Shapley value> vector, not a sufficient one.
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