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.

	Multi-car intersection Naive collisions compared to an iLQ feedback solution. Source · Docs
	Eight-player terminal-cost robot arm Cooperative joint players form a task-space terminal shape using midpoint and end-effector goals. Source · Docs
	Satellite Lady-Bandit-Guard One LQ feedback Nash strategy rolled out from many initial states. Source · Docs · spacegym-kspdg

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.robot_arm  # eight-player nonlinear terminal-cost game
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

The software/firmware is provided to you on an As-Is basis.

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