Fixation probabilities and Invasion diagram

In this notebook we analyse the Stochastic dynamics of (pairwise) social imitation under the small mutation limit (SML)

import os

import numpy as np
import matplotlib.pyplot as plt
import egttools as egt
%matplotlib inline

egt.Random.init()
seed = egt.Random._seed

Payoff matrix for a Normal Form Game

Here we will analyse a Normal Form game, so we need to first define a payoff matrix

T=4; R=2; P=1; S=0
A = np.array([
    [P, T],
    [S, R]
])

Select which strategies we want to analyse

We can add all the strategies to a list and pass it to the Game object

strategies = [egt.behaviors.NormalForm.TwoActions.Cooperator(),
              egt.behaviors.NormalForm.TwoActions.Defector(),
              egt.behaviors.NormalForm.TwoActions.TFT(),
              egt.behaviors.NormalForm.TwoActions.Pavlov(),
              egt.behaviors.NormalForm.TwoActions.Random(),
              egt.behaviors.NormalForm.TwoActions.GRIM()]

strategy_labels = [strategy.type().replace("NFGStrategies::", '') for strategy in strategies]

strategy_labels

['AllC', 'AllD', 'TFT', 'Pavlov', 'Random', 'GRIM']

Instantiate the Normal Form Game

Now we can instanciate the Game and pass both the strategies and the payoff matrix

game = egt.games.NormalFormGame(100, A, strategies)

Now we instanciate the StochDynamics class to perform analytical calculations

We pass the expected payoffs calculated by the NormalFormGame class

Z= 100; beta=1
evolver = egt.analytical.PairwiseComparison(Z, game)

transition_matrix,fixation_probabilities = evolver.calculate_transition_and_fixation_matrix_sml(beta)
stationary_distribution = egt.utils.calculate_stationary_distribution(transition_matrix.transpose())

Plot invasion diagram

fig, ax = plt.subplots(figsize=(5, 5), dpi=150)
G = egt.plotting.draw_invasion_diagram(strategy_labels,
                                              1/Z, fixation_probabilities, stationary_distribution,
                                              node_size=600,
                                              font_size_node_labels=8,
                                              font_size_edge_labels=8,
                                              font_size_sd_labels=8,
                                              edge_width=1,
                                              min_strategy_frequency=0.00001,
                                              ax=ax)
plt.axis('off')
plt.show() # display