diff --git a/tests/games.py b/tests/games.py
index c08e6497d..e34591d4d 100644
--- a/tests/games.py
+++ b/tests/games.py
@@ -100,7 +100,7 @@ def create_coord_4x4_nfg(outcome_version: bool = False) -> gbt.Game:
 # Extensive-form games (efg)
 
 
-def create_2x2_zero_sum_efg(missing_term_outcome=False) -> gbt.Game:
+def create_2x2_zero_sum_efg(missing_term_outcome: bool = False) -> gbt.Game:
     """
     EFG corresponding to 2x2 zero-sum game (I,-I).
     If missing_term_outcome, the terminal node after "T" then "r" does not have an outcome.
@@ -123,7 +123,7 @@ def create_2x2_zero_sum_efg(missing_term_outcome=False) -> gbt.Game:
     return g
 
 
-def create_matching_pennies_efg(with_neutral_outcome=False) -> gbt.Game:
+def create_matching_pennies_efg(with_neutral_outcome: bool = False) -> gbt.Game:
     """
     The version with_neutral_outcome adds a (0,0) payoff outcomes at a non-terminal node.
     """
@@ -156,7 +156,7 @@ def create_mixed_behav_game_efg() -> gbt.Game:
     return read_from_file("mixed_behavior_game.efg")
 
 
-def create_stripped_down_poker_efg(nonterm_outcomes=False) -> gbt.Game:
+def create_stripped_down_poker_efg(nonterm_outcomes: bool = False) -> gbt.Game:
     """
     Returns
     -------
@@ -404,7 +404,7 @@ def get_path(node):
     return g
 
 
-def create_kuhn_poker_efg(nonterm_outcomes=False) -> gbt.Game:
+def create_kuhn_poker_efg(nonterm_outcomes: bool = False) -> gbt.Game:
     """
     Returns
     -------
@@ -458,12 +458,15 @@ def kuhn_poker_lcp_first_mixed_strategy_prof():
     return [alice, bob]
 
 
-def create_one_shot_trust_efg() -> gbt.Game:
+def create_one_shot_trust_efg(unique_NE_variant: bool = False) -> gbt.Game:
     """
-    Returns
-    -------
-    Game
-        One-shot trust game, after Kreps (1990)
+    One-shot trust game, after Kreps (1990)
+
+    The unique_NE_variant makes Trust a dominant strategy, replacing the
+    non-singleton equilibrium component from the standard version of the game
+    where the Buyer plays "Not Trust" and the seller can play any mixture with
+    < 0.5 probability on Honor with a unique NE where the Buyer plays Trust and
+    the Seller plays Abuse.
     """
     g = gbt.Game.new_tree(
         players=["Buyer", "Seller"], title="One-shot trust game, after Kreps (1990)"
@@ -473,9 +476,14 @@ def create_one_shot_trust_efg() -> gbt.Game:
     g.set_outcome(
         g.root.children[0].children[0], g.add_outcome([1, 1], label="Trustworthy")
     )
-    g.set_outcome(
-        g.root.children[0].children[1], g.add_outcome([-1, 2], label="Untrustworthy")
-    )
+    if unique_NE_variant:
+        g.set_outcome(
+            g.root.children[0].children[1], g.add_outcome(["1/2", 2], label="Untrustworthy")
+        )
+    else:
+        g.set_outcome(
+            g.root.children[0].children[1], g.add_outcome([-1, 2], label="Untrustworthy")
+        )
     g.set_outcome(g.root.children[1], g.add_outcome([0, 0], label="Opt-out"))
     return g
 
diff --git a/tests/test_nash.py b/tests/test_nash.py
index 375169db8..388600157 100644
--- a/tests/test_nash.py
+++ b/tests/test_nash.py
@@ -95,11 +95,20 @@ def test_enummixed_rational(game: gbt.Game, mixed_strategy_prof_data: list):
             None,
         ),
         # 2-player non-zero-sum games
-        (
+        pytest.param(
             games.create_one_shot_trust_efg(),
-            [[[[0, 1]], [["1/2", "1/2"]]], [[[0, 1]], [[0, 0]]]],
-            2,
-        ),  # Note all zero probs at iset
+            [[[[0, 1]], [["1/2", "1/2"]]], [[[0, 1]], [[0, 1]]]],
+            # second entry assumes we extend to Nash using only pure behaviors
+            # currently we get [[0, 1]], [[0, 0]]] as a second eq
+            None,
+            marks=pytest.mark.xfail(reason="Problem with enumpoly, as per issue #660")
+        ),
+        pytest.param(
+            games.create_one_shot_trust_efg(unique_NE_variant=True),
+            [[[[1, 0]], [[0, 1]]]],  # currently we get [[0, 1]], [[0, 0]]] as a second eq
+            None,
+            marks=pytest.mark.xfail(reason="Problem with enumpoly, as per issue #660")
+        ),
         (
             games.create_EFG_for_nxn_bimatrix_coordination_game(3),
             [