egttools.numerical.numerical_.calculate_hypergeometric_fitness

calculate_hypergeometric_fitness()

Compute the fitness of a focal player (not included in strategies) via hypergeometric sampling.

This is the standard EGT fitness calculation for finite populations:

fitness = sum_g P(g | strategies, pop_size-1, group_size-1) * payoff(player_type, g)

where g ranges over all group configurations that include the focal player (i.e. g[player_type] >= 1), and P is the multivariate hypergeometric probability that the remaining group_size-1 slots are filled from the background population (which has strategies individuals, not including the focal player).

Parameters:

  • player_type (int) – Index of the focal player’s strategy (0-based).

  • pop_size (int) – Total population size including the focal player.

  • group_size (int) – Number of individuals in the interaction group including the focal player.

  • nb_strategies (int) – Number of distinct strategies.

  • strategies (numpy.ndarray) – Integer array of length nb_strategies with counts of each strategy in the population excluding the focal player. Must sum to pop_size - 1.

  • payoffs_row (numpy.ndarray) – Float array of length calculate_nb_states(group_size, nb_strategies) where payoffs_row[g] is the payoff of player_type in group configuration sample_simplex(g, group_size, nb_strategies).

Returns:

Expected fitness of the focal player.

Return type:

float

Examples

>>> import numpy as np
>>> import egttools as egt
>>> pop_size, group_size, nb_strategies = 10, 3, 2
>>> # Focal player is a cooperator (strategy 1), population has 5 C, 4 D (excluding focal)
>>> strategies = np.array([4, 5], dtype=np.uint64)
>>> # payoffs_row[g] = payoff of cooperator in group config g
>>> nb_configs = egt.calculate_nb_states(group_size, nb_strategies)
>>> payoffs_row = np.zeros(nb_configs)
>>> for g in range(nb_configs):
...     gc = egt.sample_simplex(g, group_size, nb_strategies)
...     payoffs_row[g] = gc[1] - 1.0  # cooperators pay cost 1
>>> egt.calculate_hypergeometric_fitness(1, pop_size, group_size, nb_strategies, strategies, payoffs_row)