Payoff Mechanism

This module defines the core class used to specify and integrate payoff mechanisms in population games.

A payoff mechanism is defined through a payoff dynamics model (PDM), which governs how payoffs evolve over time based on the current state of the system.

Numerical integration is performed using scipy.

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Payoff Mechanism

class popgames.payoff_mechanism.PayoffMechanism(h_map, n, w_map=None, d=0)[source]

Bases: object

Payoff mechanism implemented as a payoff dynamics model (PDM).

Initialize the payoff mechanism instance.

Parameters:

  • h_map (Union[Callable[[np.ndarray], np.ndarray], Callable[[np.ndarray, np.ndarray], np.ndarray]]) – Output function of the PDM.

  • n (int) – Dimensionality of the expected input vector x.

  • w_map (Callable[[np.ndarray, np.ndarray], np.ndarray], optional) – Right-hand side of the PDM dynamics.

  • None (Defaults to)

  • PDM. (corresponding to a memory-less)

  • d (int, optional) – Dimensionality of the PDM state vector x. Defaults to 0 (in the memoryless case).

integrate(q0, x0, t_span, method='Radau', output_trajectory=True)[source]

Numerically integrate the PDM.

This method relies on scipy.integrate.solve_ivp.

Parameters:

  • q0 (np.ndarray) – Initial PDM state vector of shape (d, 1).

  • x0 (np.ndarray) – Initial PDM input vector of shape (n, 1).

  • t_span (tuple) – Time span of integration.

  • method (str, optional) – Integration method. Defaults to ‘Radau’.

  • output_trajectory (bool, optional) – Whether to output the trajectory or just the final state-output pair. Defaults to True.

Returns:

Contains results of the integration as a SimpleNameSpace with keys t, q, and p, for the time, state, and output vectors, respectively.

Return type:

SimpleNamespace