I have an exercise for Shapley value. As I know how to calculate it, I have an 8-element set and it would be difficult to calculate it by hand. It is a network G(V, E), where V is the set of nodes and E set of edges.
The characteristic function on this network
$$ v: 2^v -> \mathbb{R} \\ v(C) = |C| - 1/3 \quad N(C)\quad for\quad C \in 2^v $$
where N(C) denotes numbers of neighbours of nodes in coalition C. This is the graph: Graph picture
I need to derive the formula for the Shapley value of this game, calculate its complexity and compute the Shapley value for 2 nodes from the sample network.
Would highly appreciate any help - even just a hint where to start. Thank you.
Ok, if anyone was wondering, this could be solved conveniently using https://arxiv.org/ftp/arxiv/papers/1402/1402.0567.pdf