S=shap1(n,v);

function S=shap1(n,v); 
% This program determines the shapley value .Shapley value is one of
% important solution concept for Transferable utility cooperative game cooperative game.
  m=2^n-1;
  % The 2^2-1 coalition contrains of the transferable utility game.
A=coalition(n);
ss=ones(1,n);
 A=[A' ss']';
            for k=1:n
         k1=zeros(1,m);
     k2=k1;
     A2=0*A;
        for i=1:m
            if A(i,k)>0
                k1(i)=v(i);
                A2(i,:)=A(i,:);
                 else
            end
        end
         A3=A2;
         A3(:,k)=0;
         for i=1:m
             for j=1:m
                 if A3(i,1:n)==A(j,1:n);
                     k2(i)=v(j);
                 else
               end
             end
         end
         k3=k1-k2;
         k4=sum(A2.');
         r=zeros(1,m);
         mm=factorial(n-1);
         for i=1:m
                  if k4(i)>0
             r(i)=mm./nchoosek(n-1,k4(i)-1);
             else
         end
         end
         S(k)=sum(k3.*r)/sum(r);
       end