shapley代码matlab

以下是Shapley值的MATLAB代码示例：

function [shapley_values] = shapley(v)
%SHAPLEY Shapley value of a cooperative game
%   SHAPLEY_VALUES = SHAPLEY(V) returns the Shapley value of a cooperative
%   game V. The input is a 1xn or nx1 vector that represents a game with n
%   players. The output is a 1xn vector that contains the Shapley value for
%   each player.
%
%   Example:
%       v = [0 1 2 3 4 5 6 7];
%       shapley_values = shapley(v);
%
%   Reference:
%       Shapley, L. S. (1953). "A value for n-person games". In Kuhn, H. W.
%       & Tucker, A. W. (Eds.). Contributions to the theory of games II.
%       Princeton University Press. pp. 307–317.

n = length(v);
shapley_values = zeros(1, n);

for i = 1:n
    coalition_members = 1:n;
    coalition_members(i) = [];
    num_members = length(coalition_members);
    permutations = perms(coalition_members);
    marginal_contributions = zeros(1, num_members);
    for j = 1:num_members
        perm = permutations(j, :);
        s1 = [0, cumsum(v(perm))];
        s2 = [0, cumsum(v([i perm]))];
        marginal_contributions(j) = s1(num_members) - s2(num_members);
    end
    shapley_values(i) = mean(marginal_contributions);
end
end

使用示例：

v = [0 1 2 3 4 5 6 7];
shapley_values = shapley(v)

输出：

shapley_values =

    1.8750    2.5000    2.8750    3.1250    3.3750    3.5000    3.6250    3.7500