Merge ec15121 into d73c959

quantecon/game_theory/pure_nash.py

@@ -9,13 +9,16 @@
 import numpy as np
 
 
-def pure_nash_brute(g):
+def pure_nash_brute(g, tol=None):
     """
     Find all pure Nash equilibria of a normal form game by brute force.
 
     Parameters
     ----------
     g : NormalFormGame
+    tol : scalar(float), optional(default=None)
+        Tolerance level used in determining best responses. If None,
+        default to the value of the `tol` attribute of `g`.
 
     Returns
     -------
@@ -43,16 +46,19 @@ def pure_nash_brute(g):
     []
 
     """
-    return list(pure_nash_brute_gen(g))
+    return list(pure_nash_brute_gen(g, tol=tol))
 
 
-def pure_nash_brute_gen(g):
+def pure_nash_brute_gen(g, tol=None):
     """
     Generator version of `pure_nash_brute`.
 
     Parameters
     ----------
     g : NormalFormGame
+    tol : scalar(float), optional(default=None)
+        Tolerance level used in determining best responses. If None,
+        default to the value of the `tol` attribute of `g`.
 
     Yields
     ------
@@ -61,5 +67,5 @@ def pure_nash_brute_gen(g):
 
     """
     for a in np.ndindex(*g.nums_actions):
-        if g.is_nash(a):
+        if g.is_nash(a, tol=tol):
             yield a

quantecon/game_theory/tests/test_pure_nash.py

@@ -57,6 +57,20 @@ def test_brute_force(self):
         for d in self.game_dicts:
             eq_(sorted(pure_nash_brute(d['g'])), sorted(d['NEs']))
 
+    def test_tol(self):
+        # Prisoners' Dilemma game with one NE and one epsilon NE
+        epsilon = 1e-08
+
+        PD_bimatrix = [[(1, 1), (-2, 1 + epsilon)],
+                       [(1 + epsilon, -2), (0, 0)]]
+
+        NEs = [(1, 1)]
+        epsilon_NEs = [(1, 1), (0, 0)]
+
+        g = NormalFormGame(PD_bimatrix)
+        for tol, answer in zip([0, epsilon], [NEs, epsilon_NEs]):
+            eq_(sorted(pure_nash_brute(g, tol=tol)), sorted(answer))
+
 
 if __name__ == '__main__':
     import sys