egttools.plotting.simplified.check_replicator_stability_pairwise_games¶
- check_replicator_stability_pairwise_games(stationary_points, payoff_matrix, atol_neg=0.0001, atol_pos=0.0001, atol_zero=0.0001)[source]¶
Determine the stability of stationary points for the replicator equation in pairwise games.
This function uses the Jacobian of the replicator dynamics to classify each stationary point as stable, unstable, or a saddle point based on the signs of the eigenvalues of the Jacobian.
- Parameters:
stationary_points (list of ndarray) – A list of stationary points (strategy frequency vectors), each of shape (n,).
payoff_matrix (ndarray of shape (n, n)) – Payoff matrix representing the interactions between n strategies.
atol_neg (float, optional) – Tolerance for determining if an eigenvalue is considered significantly negative.
atol_pos (float, optional) – Tolerance for determining if an eigenvalue is considered significantly positive.
atol_zero (float, optional) – Tolerance for determining if an eigenvalue is effectively zero.
- Returns:
A list where each entry corresponds to the stability classification of a stationary point:
1 for stable (all eigenvalues ≤ 0)
-1 for unstable (all eigenvalues ≥ 0)
0 for saddle (mixed signs among eigenvalues)
- Return type: