shapley值的matlab代码
时间: 2023-08-05 20:02:42 浏览: 57
以下是用 MATLAB 计算 Shapley 值的示例代码:
```matlab
function [shapley_values] = shapley_value(v)
% SHAPLEY_VALUE computes the Shapley value of the game v
% [shapley_values] = SHAPLEY_VALUE(v) returns the Shapley value of the game v,
% where v is a matrix of size (N,M) representing M players and N coalitions.
%
% Example usage:
% v = [0 1 2; 1 0 3; 2 3 0];
% shapley_values = shapley_value(v)
% Number of players
n = size(v, 2);
% Preallocate Shapley values
shapley_values = zeros(1, n);
for i = 1:n
% Compute marginal contributions
m = nchoosek(n-1, i-1); % number of possible coalitions
contributions = zeros(1, m);
k = 1;
for S = combnk(1:n-1, i-1)' % iterate over all possible coalitions
T = [S, n]; % add the i-th player to coalition S
contributions(k) = v(T) - v(S); % compute marginal contribution
k = k + 1;
end
% Compute Shapley value for player i
shapley_values(i) = sum(factorial(i-1) * factorial(n-i) / factorial(n) * contributions) ;
end
end
```
这个代码使用了 MATLAB 自带的 `nchoosek` 函数来生成所有可能的联盟,然后计算每个玩家的边际贡献并最终求和得到 Shapley 值。请注意,这个代码假设所有的玩家都是对称的,因此每个玩家的 Shapley 值相等。如果这个假设不成立,代码需要进行一些修改。
相关推荐
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)