egttools.numerical.numerical_.replicator_equation

replicator_equation()

Computes the replicator dynamics gradient for a 2-player game.

This function implements the standard replicator equation for infinite populations interacting in pairwise games. The result is a vector of growth rates (gradients) for each strategy.

Parameters:

  • frequencies (NDArray[np.float64]) – A 1D NumPy array of shape (nb_strategies,) representing the current frequency of each strategy in the population. The entries should sum to 1.

  • payoff_matrix (NDArray[np.float64]) – A 2D NumPy array of shape (nb_strategies, nb_strategies) containing payoffs. Entry [i, j] is the payoff for strategy i when interacting with j.

Returns:

A 1D NumPy array of shape (nb_strategies,) representing the replicator gradient for each strategy.

Return type:

NDArray[np.float64]

See also

egttools.replicator_equation_n_player, egttools.games.AbstractGame, egttools.numerical.PairwiseComparison, egttools.analytical.StochDynamics

Examples

>>> freqs = np.array([0.4, 0.6])
>>> A = np.array([[1, 0], [3, 2]])
>>> grad = replicator_equation(freqs, A)
>>> grad
array([-0.24,  0.24])