Calculate the Shapley value

To find the Shapley value of a game \(G = (N, v)\) use coopgt.shapley_value.calculate.

For example, for \(G = (3, v)\) with

\[ v(C) = \begin{cases} 0 & \text{if } C = \emptyset \\ 6 & \text{if } C = \{1\} \\ 12 & \text{if } C = \{2\} \\ 42 & \text{if } C = \{3\} \\ 12 & \text{if } C = \{1, 2\} \\ 42 & \text{if } C = \{1, 3\} \\ 42 & \text{if } C = \{2, 3\} \\ 42 & \text{if } C = \{1, 2, 3\} \end{cases} \]

first create the characteristic function as a dictionary:

>>> characteristic_function = {
...     (): 0,
...     (1,): 6,
...     (2,): 12,
...     (3,): 42,
...     (1, 2): 12,
...     (1, 3): 42,
...     (2, 3): 42,
...     (1, 2, 3): 42,
... }

Then compute the Shapley value:

>>> import coopgt.shapley_value
>>> shapley = coopgt.shapley_value.calculate(characteristic_function)
>>> [round(float(value), 2) for value in shapley]
[2.0, 5.0, 35.0]

The \(i\)th entry is the payoff allocated to player \(i\).