#  MAPLE.  Sept. 24, 2007
#
#  Given a payoff matrix A, use MAPLE's simplex method to
#  find the value of the corr. 2-player game.
#
# Usage:
#  Define a payoff matrix A:
#  A := Matrix(2,3,[ 1, 2, -2,    -1, -3, 4]);
#  read game;


with(simplex):

m := LinearAlgebra[RowDimension](A):
n := LinearAlgebra[ColumnDimension](A):


con := { add(y||i, i=1..m) = 1 }:

for j to n
do
   con := con union { add(A[i,j]*(y||i), i=1..m) - v1 <= 0  };

od:

con := con union { seq( y||i >= 0, i=1..m) }:

print(` Value v1 and optimal strategy y for the row player:`);
minimize( v1, con);


con := { add(x||j, j=1..n) = 1 }:

for i to m
do
   con := con union { add(-A[i,j]*(x||j), j=1..n) - v2 <= 0  };

od:

con := con union { seq( x||j >= 0, j=1..n) }:

print(` Value v2 and optimal strategy x for the column player:`);
minimize( v2, con);