.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/miscellaneous/evolutionary_game_theory.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_miscellaneous_evolutionary_game_theory.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_miscellaneous_evolutionary_game_theory.py:


========================
Evolutionary game theory
========================

`replicator equation <https://en.wikipedia.org/wiki/Replicator_equation>`__

.. warning::
    The implementation of mathematics might be wrong due to my lack of
    knowledge.

.. GENERATED FROM PYTHON SOURCE LINES 12-39



.. image-sg:: /gallery/miscellaneous/images/sphx_glr_evolutionary_game_theory_001.svg
   :alt: evolutionary game theory
   :srcset: /gallery/miscellaneous/images/sphx_glr_evolutionary_game_theory_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from mpltern.datasets import get_triangular_grid

    x = np.array(get_triangular_grid(25))

    payoff_matrix = [
        [0.0, -1.0, 1.0],
        [1.0, 0.0, -1.0],
        [-1.0, 1.0, 0.0],
    ]

    fitness = payoff_matrix @ x
    d = (fitness - np.sum(fitness * x, axis=0)) * x
    norm = np.linalg.norm(d, axis=0)

    ax = plt.subplot(projection="ternary")

    ax.tripcolor(*x, norm, cmap="turbo", shading="gouraud", rasterized=True)

    ax.quiver(*x, *d, scale=5, clip_on=False)

    ax.set_tlabel("$x_0$")
    ax.set_llabel("$x_1$")
    ax.set_rlabel("$x_2$")

    plt.show()


.. _sphx_glr_download_gallery_miscellaneous_evolutionary_game_theory.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: evolutionary_game_theory.ipynb <evolutionary_game_theory.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: evolutionary_game_theory.py <evolutionary_game_theory.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_