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Coding workflows · Exact Shapley coalition values
03
A concrete starting point
Compute exact Shapley shares for up to eight players from an integer coalition-value table bounded by 1000000 in magnitude. Test additive games and zero players, rejecting a nonzero empty coalition or a table whose length is not a power of two.
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Check the outcome
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Exact Shapley coalition values
A concrete starting point
from fractions import Fraction
from math import comb
def shapley_values(values):
if type(values) not in (list, tuple) or not 1 <= len(values) <= 256 or len(values) & (len(values)-1):
raise ValueError("shapley.table")
if any(type(v) is not int or abs(v) > 10**6 for v in values) or values[0] != 0:
raise ValueError("shapley.value")
players = len(values).bit_length()-1
result = []
for player in range(players):
share = Fraction(0)
for subset in range(len(values)):
if not subset & (1 << player):
size = subset.bit_count()
weight = Fraction(1, players*comb(players-1, size))
share += weight*(values[subset | (1 << player)]-values[subset])
result.append(share)
return resultThe example is a starting point for a real project, not a claim that generated code is already tested. Adjust paths, dependencies and expected behavior to match your application.
