#BR is the procedure that entry the matrix of n players with m avaliable decisions they 
#have, and output the best payoff for k player 
BR:=proc(M,m,n,k) local rec1,rec,champs,champs1,A,B,i,j:
A:=nops(M): B:=nops(M[1]):

if not (1<=j and j<=B) then
 print(j, `is not a valid strategy for k player`):
 RETURN(FAIL):
fi:


champs:={1}:
rec:=M[1][j][k]:

for i from 1 to A do
 #first we get the best choice of each matrix and then we compare each matrix to get the #best    choice for j player
     for h from 2 to B do
          if M[i][h][k]>rec then
          champs1:={h}:
          rec1:=M[i][h][k]:
          elif M[i][h][k]=rec1 then champs:=champus union {h}:

     fi:
     od:
     if M[i][j][k]>rec1 then

         champs:={i}:
         rec1:=M[1+m^(j-3)][j][k]:
     elif M[1+m^(j-3)][j][k]=rec then champs:=champs union {i}:
     fi:
od:
#We return the set of Champions
champs:

end:


PNEn:=proc(M,m,n,k,j) local A,B,i,h,S:
A:=nops(M):
B:=nops(M[1]):


S:={};



end: