TEST: Increase coverage on game_theory (#343)

* TEST: Add tests for mclennen_tourky.py

* TEST: Add test for exceptions in support_enumeration.py

* TEST: Add tests for vertex_enumeration.py

* FIX: Correct typo

* RFC: Change assert_allclose to assert_array_equal

quantecon/game_theory/tests/test_mclennan_tourky.py

@@ -5,8 +5,12 @@
 
 """
 import numpy as np
-from nose.tools import ok_
+from numpy.testing import assert_array_equal
+from nose.tools import ok_, raises
 from quantecon.game_theory import Player, NormalFormGame, mclennan_tourky
+from quantecon.game_theory.mclennan_tourky import (
+     _best_response_selection, _flatten_action_profile, _is_epsilon_nash
+)
 
 
 class TestMclennanTourky():
@@ -54,13 +58,102 @@ def test_pure_nash(self):
             NE, res = mclennan_tourky(d['g'], init=init, full_output=True)
             ok_(res.num_iter==1)
 
-    def test_epsilon_nash(self):
+
+class TestMclennanTourkyInvalidInputs():
+    def setUp(self):
+            self.bimatrix = [[(3, 3), (3, 2)],
+                             [(2, 2), (5, 6)],
+                             [(0, 3), (6, 1)]]
+            self.g = NormalFormGame(self.bimatrix)
+
+    @raises(TypeError)
+    def test_mclennan_tourky_invalid_g(self):
+        mclennan_tourky(self.bimatrix)
+
+    @raises(TypeError)
+    def test_mclennan_tourky_invalid_init_type(self):
+        mclennan_tourky(self.g, 1)
+
+    @raises(ValueError)
+    def test_mclennan_tourky_invalid_init_length(self):
+        mclennan_tourky(self.g, [1])
+
+
+class TestEpsilonNash():
+    def setUp(self):
+        def anti_coordination(N, v):
+            payoff_array = np.empty((2,)*N)
+            payoff_array[0, :] = 1
+            payoff_array[1, :] = 0
+            payoff_array[1].flat[0] = v
+            g = NormalFormGame((Player(payoff_array),)*N)
+            return g
+
+        def p_star(N, v):
+            # Unique symmetric NE mixed action: [p_star, 1-p_star]
+            return 1 / (v**(1/(N-1)))
+
+        def epsilon_nash_interval(N, v, epsilon):
+            # Necessary, but not sufficient, condition: lb < p < ub
+            lb = p_star(N, v) - epsilon / ((N-1)*(v**(1/(N-1))-1))
+            ub = p_star(N, v) + epsilon / (N-1)
+            return lb, ub
+
+        self.game_dicts = []
+        v = 2
+        epsilon = 1e-5
+
+        Ns = [2, 3, 4]
+        for N in Ns:
+            g = anti_coordination(N, v)
+            lb, ub = epsilon_nash_interval(N, v, epsilon)
+            d = {'g': g,
+                 'epsilon': epsilon,
+                 'lb': lb,
+                 'ub': ub}
+            self.game_dicts.append(d)
+
+        self.bimatrix = [[(3, 3), (3, 2)],
+                         [(2, 2), (5, 6)],
+                         [(0, 3), (6, 1)]]
+        self.g = NormalFormGame(self.bimatrix)
+
+    def test_epsilon_nash_with_full_output(self):
         for d in self.game_dicts:
             NE, res = \
                 mclennan_tourky(d['g'], epsilon=d['epsilon'], full_output=True)
             for i in range(d['g'].N):
                 ok_(d['lb'] < NE[i][0] < d['ub'])
 
+    def test_epsilon_nash_without_full_output(self):
+        for d in self.game_dicts:
+            NE = mclennan_tourky(d['g'], epsilon=d['epsilon'],
+                                 full_output=False)
+            for i in range(d['g'].N):
+                ok_(d['lb'] < NE[i][0] < d['ub'])
+
+    def test_is_epsilon_nash_no_indptr(self):
+        ok_(_is_epsilon_nash([1., 0., 0., 1., 0.], self.g, 1e-5))
+
+
+def test_flatten_action_profile():
+    unflattened_actions = [[1/3, 1/3, 1/3], [1/2, 1/2]]
+    flattened_actions = [1/3, 1/3, 1/3, 1/2, 1/2]
+    test_obj = _flatten_action_profile(unflattened_actions, [0, 3, 5])
+    assert_array_equal(test_obj, flattened_actions)
+
+
+def test_best_response_selection_no_indptr():
+    bimatrix = [[(3, 3), (3, 2)],
+                [(2, 2), (5, 6)],
+                [(0, 3), (6, 1)]]
+    g = NormalFormGame(bimatrix)
+
+    test_obj = _best_response_selection([1/3, 1/3, 1/3, 1/2,1/2], g)
+    expected_output = np.array([0., 1., 0., 0., 1.])
+
+    assert_array_equal(test_obj, expected_output)
+
 
 if __name__ == '__main__':
     import sys

quantecon/game_theory/tests/test_support_enumeration.py

@@ -6,7 +6,7 @@
 """
 import numpy as np
 from numpy.testing import assert_allclose
-from nose.tools import eq_
+from nose.tools import eq_, raises
 from quantecon.util import check_random_state
 from quantecon.game_theory import Player, NormalFormGame, support_enumeration
 
@@ -71,6 +71,14 @@ def test_no_error_skew_sym(self):
         NEs = support_enumeration(g)
 
 
+@raises(TypeError)
+def test_support_enumeration_invalid_g():
+    bimatrix = [[(3, 3), (3, 2)],
+                [(2, 2), (5, 6)],
+                [(0, 3), (6, 1)]]
+    support_enumeration(bimatrix)
+
+
 if __name__ == '__main__':
     import sys
     import nose

quantecon/game_theory/tests/test_vertex_enumeration.py

@@ -6,7 +6,7 @@
 """
 import numpy as np
 from numpy.testing import assert_allclose, assert_array_equal
-from nose.tools import eq_
+from nose.tools import eq_, raises
 from quantecon.game_theory import NormalFormGame, vertex_enumeration
 from quantecon.game_theory.vertex_enumeration import _BestResponsePolytope
 
@@ -46,6 +46,14 @@ def test_vertex_enumeration(self):
                     assert_allclose(action_computed, action)
 
 
+@raises(TypeError)
+def test_vertex_enumeration_invalid_g():
+    bimatrix = [[(3, 3), (3, 2)],
+                [(2, 2), (5, 6)],
+                [(0, 3), (6, 1)]]
+    vertex_enumeration(bimatrix)
+
+
 class TestBestResponsePolytope:
     def setUp(self):
         # From von Stengel 2007 in Algorithmic Game Theory
@@ -98,6 +106,15 @@ def test_best_response_polytope(self):
         assert_allclose(vertices_computed, self.vertices_P, atol=1e-15)
 
 
+@raises(TypeError)
+def test_best_response_polytope_invalid_player_instance():
+    bimatrix = [[(3, 3), (3, 2)],
+                [(2, 2), (5, 6)],
+                [(0, 3), (6, 1)]]
+    g = NormalFormGame(bimatrix)
+    _BestResponsePolytope(g)
+
+
 if __name__ == '__main__':
     import sys
     import nose