请给我Aumann-Shapley值法的matlab代码

以下是Aumann-Shapley值法的matlab代码示例：

function [aumann_shapley_values] = aumann_shapley(v)
% Aumann-Shapley value for a cooperative game.
% Inputs:
% v: a square symmetric matrix representing the worth of all possible coalitions.
% Outputs:
% aumann_shapley_values: a vector containing the Aumann-Shapley value for each player.

n = size(v,1); % number of players
aumann_shapley_values = zeros(n,1);

for i = 1:n % for each player i
    S = nchoosek(1:n-1,i-1); % all possible coalitions excluding player i
    num_S = size(S,1); % number of possible coalitions
    payoffs = zeros(num_S,1); % payoffs for each coalition
    for j = 1:num_S % for each coalition
        coalition = [S(j,:),i]; % add player i to the coalition
        payoffs(j) = sum(v(coalition,coalition)); % calculate the payoff for the coalition
    end
    aumann_shapley_values(i) = sum(payoffs.*factorial(i-1).*factorial(n-i))./factorial(n); % calculate the Aumann-Shapley value for player i
end

end

此代码实现了对任意大小的玩家集合的Aumann-Shapley值计算，其中输入矩阵v是对称矩阵（行列数相等），表示可能联盟的价值。输出是一个向量，其中第i个元素是第i个玩家的Aumann-Shapley值。