PYDGENS: Python/JAX Differential Game Equilibria Numerical Solvers

Documentation · Examples · API · Solvers · GitHub

PYDGENS provides numerical solvers for approximating equilibrium solutions in multi-player, general-sum dynamic and differential games. The package currently focuses on linear-quadratic feedback Nash games, iterative linear-quadratic methods for nonlinear games, and augmented-Lagrangian workflows for constrained games.

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Installation

pip install pydgens

PYDGENS requires Python 3.12 or newer.

Solvers

PYDGENS currently supports three main solver paths. See the solver notes for a sparse theory map and references.

Usage Example

Define and solve for the local Nash equilibrium of a nonlinear game by combining a time grid, dynamics, player costs, and player-owned control slices:

import jax.numpy as jnp
import pydgens as pdg

x0 = jnp.array([4.0, 4.0, 0.0, 0.0])  # px, py, heading, speed

game = pdg.game(
    tg=pdg.time_grid(nt=34, dt=0.1),
    dynamics=pdg.nonlinear_dynamics(
        nx=4,
        nu=2,
        dynamics=lambda t, x, u: jnp.array([
            x[3] * jnp.cos(x[2]),
            x[3] * jnp.sin(x[2]),
            u[0],
            u[1],
        ]),
    ),
    players=[
        pdg.player(
            name="turn",
            joint_ctrl_slice=slice(0, 1),
            cost=pdg.player_cost(
                running=lambda t, x, u: x[0] ** 2 + x[1] ** 2 + u[0] ** 2,
            ),
        ),
        pdg.player(
            name="speed",
            joint_ctrl_slice=slice(1, 2),
            cost=pdg.player_cost(
                running=lambda t, x, u: (x[3] - 1.0) ** 2 + u[1] ** 2,
            ),
        ),
    ],
)

solution = pdg.solve(game, x0=x0, method="ilq")
print(solution)

Further examples of solving for equilibria in differential games can be run directly with:

python -m pydgens.examples.tug_o_war  # minimal linear-quadratic (LQ) game
python -m pydgens.examples.unicycle   # nonlinear game solved with iterative method
python -m pydgens.examples.constrained_integrators  # constrained game solved Lagrangian method

A comprehensive list of examples is included in the examples documentation.

Disclaimer

DISTRIBUTION STATEMENT A. Approved for public release. Distribution is unlimited.

This material is based upon work supported by the Under Secretary of War for Research and Engineering under Air Force Contract No. FA8702-15-D-0001 or FA8702-25-D-B002. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Under Secretary of War for Research and Engineering.

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SPDX-License-Identifier: MIT

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