.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/consensus/pos/plot_02_nothing_at_stake.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_consensus_pos_plot_02_nothing_at_stake.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

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

.. _sphx_glr_api_gallery_consensus_pos_plot_02_nothing_at_stake.py:


Nothing at stake: why proof of stake needs penalties (Buterin 2014)
===================================================================

A proof-of-work miner must divide its hashrate between competing forks; a
proof-of-stake validator can sign every fork at no cost and collect the
reward whichever one wins. If everyone does that, forks never resolve.
Buterin's Slasher proposal made such double-signing punishable: evidence
of two conflicting signatures destroys the validator's deposit.

What to look for
----------------

Without a penalty, signing both forks pays more than any honest choice.
Once the penalty exceeds the reward lost by picking one side, picking a
side wins. Every modern proof-of-stake protocol has slashing.

The history behind this experiment: :doc:`/history/consensus_breakthroughs`.

.. GENERATED FROM PYTHON SOURCE LINES 22-24

Payoffs without slashing
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-33

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    import blockchainkit as bk

    free = bk.consensus.fork_voting_payoffs(0.6, reward=1.0, penalty=0.0)
    print("no penalty:", free)
    assert free["both"] > free["A"] > free["B"]





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

 .. code-block:: none

    no penalty: {'A': 0.6, 'B': 0.4, 'both': 1.0}




.. GENERATED FROM PYTHON SOURCE LINES 34-36

Payoffs as the penalty grows
----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 36-55

.. code-block:: Python

    penalties = np.linspace(0, 1.5, 61)
    rows = [bk.consensus.fork_voting_payoffs(0.6, 1.0, p) for p in penalties]
    fig, ax = plt.subplots(figsize=(7, 4))
    for strategy, color in (("A", "#2563eb"), ("B", "#64748b"), ("both", "#dc2626")):
        ax.plot(penalties, [r[strategy] for r in rows], color=color, label=f"vote {strategy}")
    crossover = 1.0 - 0.6
    ax.axvline(crossover, color="black", linestyle=":", label="penalty = reward lost by choosing")
    ax.set(
        xlabel="slashing penalty",
        ylabel="expected payoff",
        title="Slashing makes choosing a fork the best response",
    )
    ax.legend()
    fig.tight_layout()
    assert (
        bk.consensus.fork_voting_payoffs(0.6, 1.0, 0.5)["A"]
        > bk.consensus.fork_voting_payoffs(0.6, 1.0, 0.5)["both"]
    )




.. image-sg:: /api/gallery/consensus/pos/images/sphx_glr_plot_02_nothing_at_stake_001.png
   :alt: Slashing makes choosing a fork the best response
   :srcset: /api/gallery/consensus/pos/images/sphx_glr_plot_02_nothing_at_stake_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 56-62

Exercise
--------
Slashing only works while the deposit can still be taken. Explain the
long-range attack: why could keys of validators who withdrew long ago be
used to forge an alternative history, and what "weak subjectivity" asks
new nodes to trust?


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

   **Total running time of the script:** (0 minutes 0.183 seconds)


.. _sphx_glr_download_api_gallery_consensus_pos_plot_02_nothing_at_stake.py:

.. only:: html

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

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/consensus/pos/plot_02_nothing_at_stake.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_nothing_at_stake.ipynb <plot_02_nothing_at_stake.ipynb>`

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

      :download:`Download Python source code: plot_02_nothing_at_stake.py <plot_02_nothing_at_stake.py>`

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

      :download:`Download zipped: plot_02_nothing_at_stake.zip <plot_02_nothing_at_stake.zip>`


.. only:: html

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

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