def test_get_evolutionary_best_response_with_K_equal_1_against_2_defectors():
"""
We see that the expected best response against 2 defectors is:
[1, 0.45420466, 0, 0.03799109]
- the first term: indicates that when the player is playing against itself
it knows to always cooperate.
- The second term (P_CD): it will still cooperate with relatively high
probability (0.454...).
- The third term (P_DC): it will never cooperate after defecting against one
a player like itself.
- The final term (P_DD): it is very likely to defect on the occasions where
it defected and so did it's opponent (probably likely that the opponent is
defector?).
"""
opponents = [np.array([0, 0, 0, 0])] * 2
axl.seed(2)
(
best_ev_response,
hist,
history_length,
) = opt_mo.get_evolutionary_best_response(
opponents, opt_mo.get_memory_one_best_response, K=1)
expected_best_response = np.array([1, 0.45420466, 0, 0.03799109])
assert type(best_ev_response) is np.ndarray
assert len(best_ev_response) == 4
assert np.allclose(expected_best_response, best_ev_response)
def test_get_evolutionary_best_response():
axl.seed(2)
random_opponents = [[random.random() for _ in range(4)] for _ in range(1)]
best_ev_response, hist, history_length = opt_mo.get_evolutionary_best_response(
random_opponents, opt_mo.get_memory_one_best_response)
assert type(best_ev_response) is np.ndarray
assert len(best_ev_response) == 4
def obtain_payoff_matrix(opponent, K, N=4):
"""
Obtain the payoff matrix for K best response players in a population of a
total of N individuals.
"""
best_ev_response, _, _ = opt_mo.get_evolutionary_best_response(
[opponent] * (N - K), opt_mo.get_memory_one_best_response, K=K)
players = [best_ev_response, opponent]
return (
np.array(
[[opt_mo.match_utility(player, opponent) for opponent in players]
for player in players]),
best_ev_response,
)
def test_get_evolutionary_best_response_against_random_opponent():
axl.seed(2)
random_opponents = [[random.random() for _ in range(4)]]
(
best_ev_response,
hist,
history_length,
) = opt_mo.get_evolutionary_best_response(
random_opponents, opt_mo.get_memory_one_best_response)
expected_best_response = np.array([0.0, 0.0, 0.0, 0.0])
assert type(best_ev_response) is np.ndarray
assert np.allclose(expected_best_response, best_ev_response)
def test_get_evolutionary_best_response_with_K_equal_4_against_random_opponent(
):
axl.seed(2)
random_opponents = [[random.random() for _ in range(4)]]
(
best_ev_response,
hist,
history_length,
) = opt_mo.get_evolutionary_best_response(
random_opponents, opt_mo.get_memory_one_best_response, K=4)
expected_best_response = np.array([0.01547687, 0, 0, 0])
assert type(best_ev_response) is np.ndarray
assert len(best_ev_response) == 4
assert np.allclose(expected_best_response, best_ev_response, atol=1e-3)
def test_get_evolutionary_best_response_with_K_equal_10_against_2_defectors():
"""
With K = 10 and 2 defectors the best response changes from `[1, 0.45420466,
0, 0.03799109]` (for K = 1) to:
[1, 0.36819048, 1, 0.75011483]
"""
opponents = [np.array([0, 0, 0, 0])] * 2
axl.seed(2)
(
best_ev_response,
hist,
history_length,
) = opt_mo.get_evolutionary_best_response(
opponents, opt_mo.get_memory_one_best_response, K=10)
expected_best_response = np.array([1, 0.36819048, 1, 0.75011483])
assert type(best_ev_response) is np.ndarray
assert len(best_ev_response) == 4
assert np.allclose(expected_best_response, best_ev_response, atol=1e-3)