rewrite Stackelberg-eq solver in cvxpy; add degenerated test case

open_spiel/python/algorithms/stackelberg_lp.py

@@ -18,8 +18,8 @@
 """
 
 import numpy as np
+import cvxpy as cp
 
-from open_spiel.python.algorithms import lp_solver
 from open_spiel.python.algorithms.projected_replicator_dynamics import _simplex_projection
 from open_spiel.python.egt.utils import game_payoffs_array
 
@@ -51,39 +51,32 @@ def solve_stackelberg(game, is_first_leader=True):
   follower_eq_strategy = None
 
   for t in range(num_follower_strategies):
-    lp = lp_solver.LinearProgram(objective=lp_solver.OBJ_MAX)
-    for s in range(num_leader_strategies):
-      lp.add_or_reuse_variable("s_{}".format(s))
-      lp.set_obj_coeff("s_{}".format(s), leader_payoff[s, t])
-
+    p_s = cp.Variable(num_leader_strategies)
+    constraints = [p_s >= 0, p_s <= 1, cp.sum(p_s) == 1]
     for t_ in range(num_follower_strategies):
       if t_ == t:
         continue
-      lp.add_or_reuse_constraint("t_{}".format(t_), lp_solver.CONS_TYPE_GEQ)
-      for s in range(num_leader_strategies):
-        lp.set_cons_coeff("t_{}".format(t_), "s_{}".format(s),
-                          follower_payoff[s, t] - follower_payoff[s, t_])
-      lp.set_cons_rhs("t_{}".format(t_), 0.0)
-    lp.add_or_reuse_constraint("sum_to_one", lp_solver.CONS_TYPE_EQ)
-    for s in range(num_leader_strategies):
-      lp.set_cons_coeff("sum_to_one", "s_{}".format(s), 1.0)
-    lp.set_cons_rhs("sum_to_one", 1.0)
-    try:
-      leader_strategy = np.array(lp.solve())
-      leader_strategy = _simplex_projection(
-          leader_strategy.reshape(-1)).reshape(-1, 1)
-      leader_value = leader_strategy.T.dot(leader_payoff)[0, t]
-      if leader_value > leader_eq_value:
-        leader_eq_strategy = leader_strategy
-        follower_eq_strategy = t
-        leader_eq_value = leader_value
-        follower_eq_value = leader_strategy.T.dot(follower_payoff)[0, t]
-    except:  # pylint: disable=bare-except
+      constraints.append(
+          p_s @ follower_payoff[:, t_] <= p_s @ follower_payoff[:, t])
+    prob = cp.Problem(cp.Maximize(p_s @ leader_payoff[:, t]), constraints)
+    prob.solve()
+    p_s_value = p_s.value
+    if p_s_value is None:
       continue
+    leader_strategy = _simplex_projection(
+        p_s.value.reshape(-1)).reshape(-1, 1)
+    leader_value = leader_strategy.T.dot(leader_payoff)[0, t]
+    if leader_value > leader_eq_value:
+      leader_eq_strategy = leader_strategy
+      follower_eq_strategy = t
+      leader_eq_value = leader_value
+      follower_eq_value = leader_strategy.T.dot(follower_payoff)[0, t]
+
+  assert leader_eq_strategy is not None, p_mat
   if is_first_leader:
     return (leader_eq_strategy.reshape(-1), np.identity(
         num_follower_strategies)[follower_eq_strategy],
-            leader_eq_value, follower_eq_value)
+        leader_eq_value, follower_eq_value)
   else:
     return (np.identity(num_follower_strategies)[follower_eq_strategy],
             leader_eq_strategy.reshape(-1), follower_eq_value, leader_eq_value)

open_spiel/python/algorithms/stackelberg_lp_test.py

@@ -22,6 +22,8 @@
 from open_spiel.python.egt.utils import game_payoffs_array
 import pyspiel
 
+EPS = 1e-6
+
 # game instances based on Conitzer & Sandholm'06 paper
 game0 = pyspiel.create_matrix_game([[2, 4], [1, 3]], [[1, 0], [0, 1]])
 commit_strategy0 = np.array([0.5, 0.5])
@@ -32,12 +34,19 @@
 commit_strategy1 = np.array([1 / 3, 2 / 3])
 commit_value1 = 4 / 3
 
+# a game with dominated strategy
+game2 = pyspiel.create_matrix_game([[3, 9], [9, 1]],
+                                   [[0, 0], [1, 8]])
+commit_strategy2 = np.array([1.0, 0.0])
+commit_value2 = 9.0
+
 
 class StackelbergLPTest(parameterized.TestCase):
 
   @parameterized.named_parameters(
       ("game0", game0, commit_strategy0, commit_value0),
       ("game1", game1, commit_strategy1, commit_value1),
+      ("game2", game2, commit_strategy2, commit_value2)
   )
   def test_simple_games(self, game, commit_strategy, commit_value):
     leader_eq_strategy, _, leader_eq_value, _ = solve_stackelberg(game)
@@ -53,7 +62,7 @@ def test_simple_games(self, game, commit_strategy, commit_value):
         leader_nash_value = eq[0].reshape(1,
                                           -1).dot(p_mat[0]).dot(eq[1].reshape(
                                               -1, 1))
-        self.assertGreaterEqual(leader_eq_value, leader_nash_value)
+        self.assertGreaterEqual(leader_eq_value-leader_nash_value, -EPS)
 
 
 if __name__ == "__main__":