/* 

  Game theory (2 player zero sum game) in Picat.

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

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


% import util.
import mip.


main => go.


go =>
  
  Game = 
    [[ 3.0, -1.0, -3.0],
     [-2.0,  4.0, -1.0], 
     [-5.0, -6.0,  2.0]],
  Rows = Game.length,
  Cols = Game[1].length,

  X = new_list(Rows),
  X :: 0.0..100.0,

  V :: -2.0..2.0,

  % For row player:
  foreach(I in 1..Rows)
    V - sum([X[J]* Game[J,I] : J in 1..Cols])  #<= 0.0
  end,
  sum(X) #= 1.0,


  solve($[max(V)], X),

  println(v=V),
  println(x=X),

  nl.