shapley值的matlab代码

以下是 Shapley 值的 Matlab 代码示例：

function [shapley_values, total_permutations] = shapley_value(v)
% v: 1xn vector, representing the worth of each player in a coalition
% shapley_values: 1xn vector, representing the Shapley value for each player
% total_permutations: total number of permutations evaluated

n = length(v);
shapley_values = zeros(1,n);
total_permutations = 0;

for i = 1:n
    % Evaluate marginal contributions for all permutations
    marginal_contributions = zeros(1,n);
    for j = 1:n
        if j ~= i
            current_permutation = randperm(n-1) + (j < i);
            for k = 1:n-1
                if current_permutation(k) >= i
                    current_permutation(k) = current_permutation(k) + 1;
                end
            end
            coalition = sort([current_permutation(1:k-1), i, current_permutation(k:end)]);
            marginal_contributions(j) = v(coalition(end)) - v(coalition(end-1));
            total_permutations = total_permutations + 1;
        end
    end
    % Average marginal contributions across all permutations
    shapley_values(i) = mean(marginal_contributions);
end

end

该函数采用一个长度为 n 的向量 v，表示每个玩家在联盟中的价值。通过随机生成所有可能的排列并计算每个玩家对每个排列的边际贡献来计算 Shapley 值。最后，平均边际贡献以获得每个玩家的 Shapley 值。函数返回每个玩家的 Shapley 值和评估的总排列数。