Revision Protocol

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Base Class

The abstract base class for all revision protocols is defined below.

class popgames.revision_protocol.RevisionProtocolABC

Bases: ABC

Abstract base class for revision protocols.

abstractmethod __call__(p, x)

Subclasses must implement this method to enable the revision protocol to be called as a function.

Parameters:

• p (np.ndarray) – The payoff vector with shape (n, 1).

• x (np.ndarray) – The population state vector with shape (n, 1).

Returns:

The switching probabilities as a matrix with shape (n, n).

Return type:

np.ndarray

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Softmax Revision Protocol

class popgames.revision_protocol.Softmax(eta)

Bases: RevisionProtocolABC

Softmax revision protocol. Also known as Logit-Choice revision protocol.

Initialize the Softmax revision protocol object.

Parameters:

eta (float) – The temperature or noise parameter.

__call__(p, x)

Evaluate the Softmax revision protocol.

Parameters:

• p (np.ndarray) – The payoff vector with shape (n, 1).

• x (np.ndarray) – The population state vector with shape (n, 1).

Returns:

The switching probabilities as a matrix with shape (n, n).

Return type:

np.ndarray

Examples

>>> import numpy as np
>>> from popgames.revision_protocol import Softmax
>>> softmax = Softmax(eta=1)
>>> p = np.array([1, -1, 2]).reshape(3, 1)
>>> x = np.array([0.1, 0.7, 0.2]).reshape(3, 1)
>>> softmax(p, x)
array([[0.25949646, 0.25949646, 0.25949646],
       [0.03511903, 0.03511903, 0.03511903],
       [0.70538451, 0.70538451, 0.70538451]])

—

Brown-von Neumann-Nash (BNN) Revision Protocol

class popgames.revision_protocol.BNN(scale)

Bases: RevisionProtocolABC

Brown-von Neumann-Nash (BNN) revision protocol.

Initialize the BNN revision protocol object.

Parameters:

scale (float) – The scale parameter to ensure well-posed probabilities.

__call__(p, x)

Evaluate the BNN revision protocol.

Parameters:

• p (np.ndarray) – The payoff vector with shape (n, 1).

• x (np.ndarray) – The population state vector with shape (n, 1).

Returns:

The switching probabilities as a matrix with shape (n, n).

Return type:

np.ndarray

Examples

>>> import numpy as np
>>> from popgames.revision_protocol import BNN
>>> bnn = BNN(scale=0.1)
>>> p = np.array([1, -1, 2]).reshape(3, 1)
>>> x = np.array([0.1, 0.7, 0.2]).reshape(3, 1)
>>> bnn(p, x)
array([[0.12, 0.12, 0.12],
       [0.  , 0.  , 0.  ],
       [0.22, 0.22, 0.22]])

–

Smith Revision Protocol

class popgames.revision_protocol.Smith(scale)

Bases: RevisionProtocolABC

Smith revision protocol.

Initialize the Smith revision protocol object.

Parameters:

scale (float) – The scale parameter to ensure well-posed probabilities.

__call__(p, x)

Evaluate the Smith revision protocol.

Parameters:

• p (np.ndarray) – The payoff vector with shape (n, 1).

• x (np.ndarray) – The population state vector with shape (n, 1).

Returns:

The switching probabilities as a matrix with shape (n, n).

Return type:

np.ndarray

Examples

>>> import numpy as np
>>> from popgames.revision_protocol import Smith
>>> smith = Smith(scale=0.1)
>>> p = np.array([1, -1, 2]).reshape(3, 1)
>>> x = np.array([0.1, 0.7, 0.2]).reshape(3, 1)
>>> smith(p, x)
array([[0. , 0.2, 0. ],
       [0. , 0. , 0. ],
       [0.1, 0.3, 0. ]])