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FIX: Player.is_dominated: Fix warnings #504

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Sep 3, 2019
Merged

FIX: Player.is_dominated: Fix warnings #504

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9eabc25
FIX: Player.is_dominated: Fix warnings
oyamad Sep 2, 2019
aa35e3c
EHN: Player.is_dominated: Add `'revised simplex'` method
oyamad Sep 2, 2019
f348e23
Merge branch 'master' into fix-gt-warning
mmcky Sep 3, 2019
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33 changes: 17 additions & 16 deletions quantecon/game_theory/normal_form_game.py
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Original file line number Diff line number Diff line change
Expand Up @@ -436,9 +436,9 @@ def is_dominated(self, action, tol=None, method=None):
method : str, optional(default=None)
If None, `lemke_howson` from `quantecon.game_theory` is used
to solve for a Nash equilibrium of an auxiliary zero-sum
game. If `method` is set to `'simplex'` or
`'interior-point'`, `scipy.optimize.linprog` is used with
the method as specified by `method`.
game. If `method` is set to `'simplex'`, `'interior-point'`,
or `'revised simplex'`, then `scipy.optimize.linprog` is
used with the method as specified by `method`.

Returns
-------
Expand Down Expand Up @@ -469,20 +469,21 @@ def is_dominated(self, action, tol=None, method=None):
g_zero_sum = NormalFormGame([Player(D), Player(-D.T)])
NE = lemke_howson(g_zero_sum)
return NE[0] @ D @ NE[1] > tol
elif method in ['simplex', 'interior-point']:
elif method in ['simplex', 'interior-point', 'revised simplex']:
from scipy.optimize import linprog
m, n = D.shape
A = np.empty((n+2, m+1))
A[:n, :m] = -D.T
A[:n, -1] = 1 # Slack variable
A[n, :m], A[n+1, :m] = 1, -1 # Equality constraint
A[n:, -1] = 0
b = np.empty(n+2)
b[:n] = 0
b[n], b[n+1] = 1, -1
A_ub = np.empty((n, m+1))
A_ub[:, :m] = -D.T
A_ub[:, -1] = 1 # Slack variable
b_ub = np.zeros(n)
A_eq = np.empty((1, m+1))
A_eq[:, :m] = 1 # Equality constraint
A_eq[:, -1] = 0
b_eq = np.ones(1)
c = np.zeros(m+1)
c[-1] = -1
res = linprog(c, A_ub=A, b_ub=b, method=method)
res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq,
method=method)
if res.success:
return res.x[-1] > tol
elif res.status == 2: # infeasible
Expand All @@ -507,9 +508,9 @@ def dominated_actions(self, tol=None, method=None):
method : str, optional(default=None)
If None, `lemke_howson` from `quantecon.game_theory` is used
to solve for a Nash equilibrium of an auxiliary zero-sum
game. If `method` is set to `'simplex'` or
`'interior-point'`, `scipy.optimize.linprog` is used with
the method as specified by `method`.
game. If `method` is set to `'simplex'`, `'interior-point'`,
or `'revised simplex'`, then `scipy.optimize.linprog` is
used with the method as specified by `method`.

Returns
-------
Expand Down
4 changes: 2 additions & 2 deletions quantecon/game_theory/tests/test_normal_form_game.py
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Original file line number Diff line number Diff line change
Expand Up @@ -13,7 +13,7 @@

# Player #

LP_METHODS = [None, 'simplex', 'interior-point']
LP_METHODS = [None, 'simplex', 'interior-point', 'revised simplex']


class TestPlayer_1opponent:
Expand Down Expand Up @@ -162,7 +162,7 @@ def test_player_corner_cases():
for method in LP_METHODS:
eq_(player.is_dominated(action, method=method), False)

e = 1e-8
e = 1e-8 * 2
player = Player([[-e, -e], [1, -1], [-1, 1]])
action = 0
eq_(player.is_best_response(action, [1/2, 1/2], tol=e), True)
Expand Down