game_theory: Add random game generators

quantecon/game_theory/__init__.py

@@ -4,3 +4,4 @@
 """
 from .normal_form_game import Player, NormalFormGame
 from .normal_form_game import pure2mixed, best_response_2p
+from .random import random_game, covariance_game

quantecon/game_theory/random.py

@@ -0,0 +1,100 @@
+"""
+Filename: random.py
+
+Author: Daisuke Oyama
+
+Generate random NormalFormGame instances.
+
+"""
+import numpy as np
+
+from .normal_form_game import Player, NormalFormGame
+from ..util import check_random_state
+
+
+def random_game(nums_actions, random_state=None):
+    """
+    Return a random NormalFormGame instance where the payoffs are drawn
+    independently from the uniform distribution on [0, 1).
+
+    Parameters
+    ----------
+    nums_actions : tuple(int)
+        Tuple of the numbers of actions, one for each player.
+
+    random_state : scalar(int) or np.random.RandomState,
+                   optional(default=None)
+        Random seed (integer) or np.random.RandomState instance to set
+        the initial state of the random number generator for
+        reproducibility. If None, a randomly initialized RandomState is
+        used.
+
+    Returns
+    -------
+    g : NormalFormGame
+
+    """
+    N = len(nums_actions)
+    if N == 0:
+        raise ValueError('nums_actions must be non-empty')
+
+    random_state = check_random_state(random_state)
+    players = [
+        Player(random_state.random_sample(nums_actions[i:]+nums_actions[:i]))
+        for i in range(N)
+    ]
+    g = NormalFormGame(players)
+    return g
+
+
+def covariance_game(nums_actions, rho, random_state=None):
+    """
+    Return a random NormalFormGame instance where the payoff profiles
+    are drawn independently from the standard multi-normal with the
+    covariance of any pair of payoffs equal to `rho`, as studied in
+    [1]_.
+
+    Parameters
+    ----------
+    nums_actions : tuple(int)
+        Tuple of the numbers of actions, one for each player.
+
+    rho : scalar(float)
+        Covariance of a pair of payoff values. Must be in [-1/(N-1), 1],
+        where N is the number of players.
+
+    random_state : scalar(int) or np.random.RandomState,
+                   optional(default=None)
+        Random seed (integer) or np.random.RandomState instance to set
+        the initial state of the random number generator for
+        reproducibility. If None, a randomly initialized RandomState is
+        used.
+
+    Returns
+    -------
+    g : NormalFormGame
+
+    References
+    ----------
+    .. [1] Y. Rinott and M. Scarsini, "On the Number of Pure Strategy
+       Nash Equilibria in Random Games," Games and Economic Behavior
+       (2000), 274-293.
+
+    """
+    N = len(nums_actions)
+    if N <= 1:
+        raise ValueError('length of nums_actions must be at least 2')
+    if not (-1 / (N - 1) <= rho <= 1):
+        lb = '-1' if N == 2 else '-1/{0}'.format(N-1)
+        raise ValueError('rho must be in [{0}, 1]'.format(lb))
+
+    mean = np.zeros(N)
+    cov = np.empty((N, N))
+    cov.fill(rho)
+    cov[range(N), range(N)] = 1
+
+    random_state = check_random_state(random_state)
+    payoff_profile_array = \
+        random_state.multivariate_normal(mean, cov, nums_actions)
+    g = NormalFormGame(payoff_profile_array)
+    return g

quantecon/game_theory/tests/test_random.py

@@ -0,0 +1,72 @@
+"""
+Filename: test_random.py
+Author: Daisuke Oyama
+
+Tests for game_theory/random.py
+
+"""
+import numpy as np
+from numpy.testing import assert_allclose, assert_raises
+from nose.tools import eq_
+
+from quantecon.game_theory import random_game, covariance_game
+
+
+def test_random_game():
+    nums_actions = (2, 3, 4)
+    g = random_game(nums_actions)
+    eq_(g.nums_actions, nums_actions)
+
+
+def test_covariance_game():
+    nums_actions = (2, 3, 4)
+    N = len(nums_actions)
+
+    rho = 0.5
+    g = covariance_game(nums_actions, rho=rho)
+    eq_(g.nums_actions, nums_actions)
+
+    rho = 1
+    g = covariance_game(nums_actions, rho=rho)
+    for a in np.ndindex(*nums_actions):
+        for i in range(N-1):
+            payoff_profile = g.payoff_profile_array[a]
+            assert_allclose(payoff_profile[i], payoff_profile[-1])
+
+    rho = -1 / (N - 1)
+    g = covariance_game(nums_actions, rho=rho)
+    for a in np.ndindex(*nums_actions):
+        assert_allclose(g.payoff_profile_array.sum(axis=-1),
+                        np.zeros(nums_actions),
+                        atol=1e-10)
+
+
+def test_random_game_value_error():
+    nums_actions = ()  # empty
+    assert_raises(ValueError, random_game, nums_actions)
+
+
+def test_covariance_game_value_error():
+    nums_actions = ()  # empty
+    assert_raises(ValueError, covariance_game, nums_actions, rho=0)
+
+    nums_actions = (2,)  # length one
+    assert_raises(ValueError, covariance_game, nums_actions, rho=0)
+
+    nums_actions = (2, 3, 4)
+
+    rho = 1.1  # > 1
+    assert_raises(ValueError, covariance_game, nums_actions, rho)
+
+    rho = -1  # < -1/(N-1)
+    assert_raises(ValueError, covariance_game, nums_actions, rho)
+
+
+if __name__ == '__main__':
+    import sys
+    import nose
+
+    argv = sys.argv[:]
+    argv.append('--verbose')
+    argv.append('--nocapture')
+    nose.main(argv=argv, defaultTest=__file__)