/*

  Game theory in Comet.

  2 player zero sum game.

  From Taha, Operations Research (8'th edition), page 528. 


  This Comet model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
  Also, see my Comet page: http://www.hakank.org/comet 

*/

import cotln;
int t0 = System.getCPUTime();

int rows = 3;
int cols = 3;
float game[1..rows, 1..cols] = 
[ 
 [3.0, -1.0, -3.0],
 [-2.0,  4.0, -1.0], 
 [-5.0, -6.0,  2.0]
];
                           

Solver<MIP> m1("lp_solve");
var<MIP>{float} x1[1..rows](m1,0,1); // row player
// var<MIP>{float} x2[1..cols](m1,0,1); // column player dual problem
var<MIP>{float} v(m1, -2,2);


// 
// Row player
//
maximize<m1> v subject to {

  // For row player:
  forall(i in 1..rows) 
    m1.post(v - sum(j in 1..cols) (x1[j]* game[j,i]) <= 0);

  m1.post(sum(i in 1..rows) x1[i] == 1);

  /*
  // column player: 
  // This is the dual problem using the same v.
  // Gives the same result as the one below.
  forall(i in 1..cols) 
    m1.post(v - sum(j in 1..cols) (x2[j]* game[i,j]) >= 0);

  m1.post(sum(i in 1..cols) x2[i] == 1);
  */

} 


cout << "row player:" << endl;
cout << "v: " << v.getValue() << endl;
cout << "Strategies: ";
forall(i in 1..rows)
  cout << x1[i].getValue() << " ";
cout << endl;


//
// Column player
//
// Instead of using the duality of the two problems,
// here we separates the problem for the column player.
// In part because we can. :-)
//
Solver<MIP> m2("lp_solve");
var<MIP>{float} x2[1..cols](m2,0,1); // column player
var<MIP>{float} v2(m2, -2,2);
minimize<m2> v subject to {

  forall(i in 1..cols) 
    m2.post(v2 - sum(j in 1..cols) (x2[j]* game[i,j]) >= 0);

  m2.post(sum(i in 1..cols) x2[i] == 1);

} 


cout << "\ncolumn player:" << endl;
cout << "v2: " << v2.getValue() << endl;
cout << "Strategies: ";
forall(i in 1..cols)
  cout << x2[i].getValue() << " ";
cout << endl;

    
int t1 = System.getCPUTime();
cout << "time:      " << (t1-t0) << endl;