Add pairwise interaction fitness function

src/ludics/fitness_functions.py

@@ -86,3 +86,35 @@ def general_four_state_fitness_function(state, **kwargs):
     return np.array(
         [sym.Function(f"f_{i + 1}")(state_symbol) for i, j in enumerate(state)]
     )
+
+def pairwise_interaction_fitness_function(state,a,b,c,d):
+    """
+    Returns the fitness of players in a symmetric pairwise interaction game. 
+    The payoff matrix for the row player is given by:
+
+    |   |  C  |  D  | 
+    |---|-----|-----|
+    | C | a_i | b_i |
+    | D | c_i | d_i |
+
+    And a player's fitness is given by the mean payoff they receive when
+    interacting in a 2 player game with a random other member of the 
+    population.
+
+    Parameters:
+    -----------
+    state: numpy.array, the ordered set of actions each player takes. 1 is a
+    cooperator, 0 is a defector,
+
+    a,b,c,d: float numpy.array, the entries to go into the payoff matrix. Entry i is the
+    respective payoff for player i's payoff matrix. Float values indicate a symmetric game
+
+    Returns:
+    ---------
+    numpy.array: an ordered array of each player's fitness
+    """
+    N = len(state)
+    number_of_cooperators = np.sum(state)
+    cooperator_payoffs = ((number_of_cooperators-1) * a + (N - number_of_cooperators) * b)/(N-1)
+    defector_payoffs = ((number_of_cooperators) * c + (N - number_of_cooperators-1) * d)/(N-1)
+    return cooperator_payoffs * state + defector_payoffs * (1 - state)

tests/test_fitness_functions.py

@@ -243,4 +243,54 @@ def test_public_goods_game_fitness_function_for_homoogeneous_contribution_and_he
 
     expected_return = np.array([0,1,2])
 
-    np.testing.assert_allclose(actual_return, expected_return)
+    np.testing.assert_allclose(actual_return, expected_return)
+
+def test_pairwise_interaction_fitness_function_for_symmetric_prisoners_dilemma():
+    """
+    Tests that pairwise_interaction_fitness_function returns the correct
+    value for a symmetric, standard prisoner's dilemma"""
+
+    state = np.array([0,1,1,0,1])
+    a = np.array([3 for _ in state])
+    b = np.array([0 for _ in state])
+    c = np.array([5 for _ in state])
+    d = np.array([1 for _ in state])
+
+    actual_value = ludics.fitness_functions.pairwise_interaction_fitness_function(state=state,a=a,b=b,c=c,d=d)
+    expected_value = np.array([4, 6/4, 6/4, 4, 6/4])
+
+    np.testing.assert_allclose(actual_value, expected_value)
+
+def test_pairwise_interaction_fitness_function_for_asymmetric_game():
+    """
+    Tests that pairwise_interaction_fitness_function returns the correct value for
+    an asymmetric game"""
+
+    state = np.array([1,0,1,0])
+    a = np.array([1,2,3,4])
+    b = np.array([2,4,6,8])
+    c = np.array([5,4,3,2])
+    d = np.array([2,2,2,1])
+
+    actual_value = ludics.fitness_functions.pairwise_interaction_fitness_function(state=state,a=a,b=b,c=c,d=d)
+
+    expected_value = np.array([5/3, 10/3, 5, 5/3])
+
+    np.testing.assert_allclose(actual_value, expected_value)
+
+def test_pairwise_interaction_fitness_function_for_mixed_parameters():
+    """
+    Tests that pairwise_interaction_fitness_function returns the correct value for
+    an asymmetric game where two parameters are symmetric"""
+
+    state = np.array([1,0,0,1])
+    a = np.array([1,2,3,4])
+    b = np.array([2,4,6,4])
+    c = 5
+    d = 2
+
+    actual_value = ludics.fitness_functions.pairwise_interaction_fitness_function(state=state,a=a,b=b,c=c,d=d)
+
+    expected_value = np.array([5/3, 4, 4, 4])
+
+    np.testing.assert_allclose(actual_value, expected_value)