/* 

  Game theory problem in Picat.

  From http://www.ms.uky.edu/~mathecon/ma416
  Vanderbei "Linear Programming - Foundations - and Extensions", 
  page 174ff


  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 =>
  
  % payoff matrix
  A = 
   [[0.0,  1.0, -2.0],
    [-3.0,  0.0,  4.0],
    [5.0, -6.0,  0.0]],

  N = A.length,

  X = new_list(N),
  X :: 0.0..1.0,
  W :: -1.0..1.0,

  foreach(I in 1..N)
     sum([A[I,J]*X[J]-W : J in 1..N]) #>=0.0
  end,

  % subject to probability:
  sum(X) #= 1.0,

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

  println(w=W),
  println(x=X),

  nl.