shapley值的matlab代码

以下是计算Shapley值的Matlab代码示例：

假设有4个玩家，每个玩家都有一个对应的贡献值向量，向量中的每个元素表示该玩家对某个任务的贡献值。我们可以使用以下代码计算Shapley值：

function shapley_values = calculate_shapley_values(contributions)
% contributions: n x m matrix, where n is the number of players and m is the number of tasks

n = size(contributions, 1); % number of players
m = size(contributions, 2); % number of tasks

% calculate factorial function
factorial_table = zeros(1, m);
for i = 1:m
    factorial_table(i) = factorial(i-1);
end

shapley_values = zeros(1, n);

% iterate over all possible permutations of players
for perm = perms(1:n)'
    for i = 1:n
        if i == 1
            coalition = perm(i);
            marginal_contribution = contributions(coalition, :);
        else
            coalition = perm(1:i-1);
            remaining_players = perm(i:end);
            % calculate the average marginal contribution of the remaining players
            average_marginal_contribution = mean(contributions(remaining_players, :)-marginal_contribution);
            % calculate the number of permutations that include the remaining players
            num_permutations = factorial_table(m-i+1)*factorial_table(i-1);
            % add the weighted average marginal contribution to the Shapley value
            shapley_values(coalition) = shapley_values(coalition) + num_permutations*average_marginal_contribution;
            % update the marginal contribution
            marginal_contribution = marginal_contribution + contributions(perm(i), :);
        end
    end
end

% normalize the Shapley values
shapley_values = shapley_values/factorial(m);
end

对于给定的贡献值矩阵，可以通过调用`calculate_shapley_values`函数来计算Shapley值。例如，如果贡献值矩阵为：

contributions = [1 2 3 4; 2 3 4 5; 3 4 5 6; 4 5 6 7];

则可以通过以下代码计算Shapley值：

shapley_values = calculate_shapley_values(contributions);

此代码将输出一个包含4个元素的向量，每个元素表示对应玩家的Shapley值。