= Induced subgraph game with self-loops
{title2=$v(S)=\sum_{i\in S}\ell_i+\sum_{\{i,j\}\subseteq S,\ i\ne j}w_{ij}$}
An <induced subgraph game> extended by one <self-loop> weight $\ell_i$ per player. Each loop is counted once, so $v(\{i\})=\ell_i$ and
$$
w_{ij}=v(\{i,j\})-v(\{i\})-v(\{j\}).
$$
Singleton and pair <coalition> values determine all weights; larger <coalition> values must then agree with their sums. Signed weights are allowed. For example, two loops of weight $1$ joined by an <edge> of weight $-1$ represent the <simple cooperative game> in which any <coalition> meeting those two players wins.
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