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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_game_theory_plot_core.py:


The Core: A Different View on Explanation
=========================================

This example introduces the game-theoretic concept of the *core* and the
*egalitarian least core* (ELC), and shows how to compute them with
:class:`~shapiq.ExactComputer`.

.. GENERATED FROM PYTHON SOURCE LINES 9-16

.. code-block:: Python


    from __future__ import annotations

    import numpy as np

    import shapiq








.. GENERATED FROM PYTHON SOURCE LINES 17-44

The Paper Game
--------------
Three AI researchers (Alice, Bob, Charlie) co-author a paper that wins a
$500 best-paper award. We model their joint productivity as a cooperative
game:

=========================  =====
Coalition                  Award
=========================  =====
{}                         $0
{Alice}                    $0
{Bob}                      $0
{Charlie}                  $0
{Alice, Bob}               $500
{Alice, Charlie}           $400
{Bob, Charlie}             $350
{Alice, Bob, Charlie}      $500
=========================  =====

Shapley values give: Alice=$200, Bob=$175, Charlie=$125. But Alice and Bob
could earn $250 each by excluding Charlie -- so the **core is empty**.

The Least Core and ELC
~~~~~~~~~~~~~~~~~~~~~~
The *least core* finds the minimum subsidy :math:`e` that makes cooperation
stable. The *egalitarian least core* picks the distribution with minimum
:math:`\|x\|_2` from the least core.

.. GENERATED FROM PYTHON SOURCE LINES 44-66

.. code-block:: Python



    class PaperGame(shapiq.Game):
        def __init__(self) -> None:
            super().__init__(n_players=3, normalize=True, normalization_value=0)

        def value_function(self, coalitions: np.ndarray) -> np.ndarray:
            values = {
                (): 0,
                (0,): 0,
                (1,): 0,
                (2,): 0,
                (0, 1): 500,
                (0, 2): 400,
                (1, 2): 350,
                (0, 1, 2): 500,
            }
            return np.array([values[tuple(np.where(x)[0])] for x in coalitions])


    paper_game = PaperGame()








.. GENERATED FROM PYTHON SOURCE LINES 67-69

Computing the Egalitarian Least Core
-------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 69-75

.. code-block:: Python


    exact_computer = shapiq.ExactComputer(n_players=3, game=paper_game)
    elc = exact_computer("ELC")
    print("ELC payoffs:", elc.dict_values)
    print("Stability subsidy e*:", exact_computer._elc_stability_subsidy)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    ELC payoffs: {(0,): 233.33333333333323, (1,): 183.33333333333337, (2,): 83.33333333333336}
    Stability subsidy e*: 83.33333333333341




.. GENERATED FROM PYTHON SOURCE LINES 76-78

The ELC distributes approximately: Alice $233, Bob $183, Charlie $83,
with a stability subsidy of about $83.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.017 seconds)


.. _sphx_glr_download_auto_examples_game_theory_plot_core.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_core.zip <plot_core.zip>`