egttools.analytical.sed_analytical.replicator_equation_n_player

replicator_equation_n_player(x, payoffs, group_size)[source]

Compute the replicator dynamics for N-player games.

In N-player games, fitness is computed as the expected payoff over all possible group configurations of co-players. This function computes the discrete time gradient of strategy frequencies under this setting.

Parameters:

  • x (ndarray of shape (n,)) – Current frequency distribution over n strategies.

  • payoffs (ndarray of shape (n, m)) – Payoff matrix where each row represents a strategy, and each column a group configuration. Entry [i, j] gives the expected payoff of strategy i in group configuration j.

  • group_size (int) – Number of individuals in each interacting group.

Returns:

Time derivative (gradient) of strategy frequencies under replicator dynamics.

Return type:

ndarray of shape (n,)