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game_theory_taha

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/game_theory_taha.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/examples/contrib/game_theory_taha.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python

%pip install ortools

Game theory in Google or-tools.

2 player zero sum game.

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

This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

python

import sys
from ortools.linear_solver import pywraplp


def main(sol='CBC'):

  # Create the solver.
  solver = pywraplp.Solver.CreateSolver(sol)
  if not solver:
    return

  # data
  rows = 3
  cols = 3

  game = [[3.0, -1.0, -3.0], [-2.0, 4.0, -1.0], [-5.0, -6.0, 2.0]]

  #
  # declare variables
  #

  #
  # row player
  #
  x1 = [solver.NumVar(0, 1, 'x1[%i]' % i) for i in range(rows)]

  v = solver.NumVar(-2, 2, 'v')

  for i in range(rows):
    solver.Add(v - solver.Sum([x1[j] * game[j][i] for j in range(cols)]) <= 0)

  solver.Add(solver.Sum(x1) == 1)

  objective = solver.Maximize(v)

  solver.Solve()

  print()
  print('row player:')
  print('v = ', solver.Objective().Value())
  print('Strategies: ')
  for i in range(rows):
    print(x1[i].SolutionValue(), end=' ')
  print()
  print()

  #
  # For column player:
  #
  x2 = [solver.NumVar(0, 1, 'x2[%i]' % i) for i in range(cols)]

  v2 = solver.NumVar(-2, 2, 'v2')

  for i in range(cols):
    solver.Add(v2 - solver.Sum([x2[j] * game[i][j] for j in range(rows)]) >= 0)

  solver.Add(solver.Sum(x2) == 1)

  objective = solver.Minimize(v2)

  solver.Solve()

  print()
  print('column player:')
  print('v2 = ', solver.Objective().Value())
  print('Strategies: ')
  for i in range(rows):
    print(x2[i].SolutionValue(), end=' ')
  print()

  print()
  print('walltime  :', solver.WallTime(), 'ms')
  print('iterations:', solver.Iterations())
  print()


sol = 'CBC'
if len(sys.argv) > 1:
  sol = sys.argv[1]
  if sol != 'GLPK' and sol != 'CBC':
    print('Solver must be either GLPK or CBC')
    sys.exit(1)

main(sol)