计算Shapley值的matlab

计算Shapley值的matlab可以使用以下代码：

function [shapley_values, ~] = shapley_value(game, valuation)
% game: n x m matrix representing the characteristic function of the game
% valuation: 1 x n vector representing the valuation of each player

n = size(game, 1);
shapley_values = zeros(1, n);

for i = 1:n
    contributions = zeros(1, n);
    for S = bitarray(n-1)
        if S(i) == 1
            continue
        end
        coalition = [find(S), i];
        m = length(coalition);
        if m == 1
            contributions(coalition) = contributions(coalition) + valuation(coalition);
        else
            for j = 1:m
                subset = coalition;
                subset(j) = [];
                contributions(coalition(j)) = contributions(coalition(j)) + (game(coalition, S) - game(subset, S)) / factorial(m-1) * valuation(coalition);
            end
        end
    end
    shapley_values(i) = sum(contributions) / n;
end

end

function A = bitarray(n)
% generate all possible n-bit arrays
% e.g. bitarray(3) returns [0 0 0; 0 0 1; 0 1 0; 0 1 1; 1 0 0; 1 0 1; 1 1 0; 1 1 1]

if n == 1
    A = [0; 1];
else
    A = [zeros(2^(n-1), 1), bitarray(n-1); ones(2^(n-1), 1), bitarray(n-1)];
end

end

其中，`game`是一个$n\times m$的矩阵，表示合作博弈的特征函数；`valuation`是一个$1\times n$的向量，表示每个玩家的价值。函数返回每个玩家的Shapley值。