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$α$-Potential Games for Decentralized Control of Connected and Automated Vehicles

Xuan Di, Anran Hu, Zhexin Wang, Yufei Zhang

TL;DR

This work introduces an α-potential game framework to address decentralized control of heterogeneous connected and automated vehicles (CAVs) in finite populations. It shows that computing an α-Nash equilibrium reduces to solving a decentralized closed-loop control problem and derives tight α-bounds based on interaction intensity and asymmetry, enabling accurate modeling of local, collision-prone interactions beyond mean-field assumptions. A scalable policy-gradient algorithm with decentralized neural-network policies is developed to compute α-NEs, and extensive simulations demonstrate effective collision avoidance, obstacle handling, and heterogeneity among vehicle types. The approach offers a practical, scalable alternative to mean-field methods for realistic CAV traffic, capable of capturing strong, local interactions in finite populations.

Abstract

Designing scalable and safe control strategies for large populations of connected and automated vehicles (CAVs) requires accounting for strategic interactions among heterogeneous agents under decentralized information. While dynamic games provide a natural modeling framework, computing Nash equilibria (NEs) in large-scale settings remains challenging, and existing mean-field game approximations rely on restrictive assumptions that fail to capture collision avoidance and heterogeneous behaviors. This paper proposes an $α$-potential game framework for decentralized CAV control. We show that computing $α$-NE reduces to solving a decentralized control problem, and derive tight bounds of the parameter $α$ based on interaction intensity and asymmetry. We further develop scalable policy gradient algorithms for computing $α$-NEs using decentralized neural-network policies. Numerical experiments demonstrate that the proposed framework accommodates diverse traffic flow models and effectively captures collision avoidance, obstacle avoidance, and agent heterogeneity.

$α$-Potential Games for Decentralized Control of Connected and Automated Vehicles

TL;DR

This work introduces an α-potential game framework to address decentralized control of heterogeneous connected and automated vehicles (CAVs) in finite populations. It shows that computing an α-Nash equilibrium reduces to solving a decentralized closed-loop control problem and derives tight α-bounds based on interaction intensity and asymmetry, enabling accurate modeling of local, collision-prone interactions beyond mean-field assumptions. A scalable policy-gradient algorithm with decentralized neural-network policies is developed to compute α-NEs, and extensive simulations demonstrate effective collision avoidance, obstacle handling, and heterogeneity among vehicle types. The approach offers a practical, scalable alternative to mean-field methods for realistic CAV traffic, capable of capturing strong, local interactions in finite populations.

Abstract

Designing scalable and safe control strategies for large populations of connected and automated vehicles (CAVs) requires accounting for strategic interactions among heterogeneous agents under decentralized information. While dynamic games provide a natural modeling framework, computing Nash equilibria (NEs) in large-scale settings remains challenging, and existing mean-field game approximations rely on restrictive assumptions that fail to capture collision avoidance and heterogeneous behaviors. This paper proposes an -potential game framework for decentralized CAV control. We show that computing -NE reduces to solving a decentralized control problem, and derive tight bounds of the parameter based on interaction intensity and asymmetry. We further develop scalable policy gradient algorithms for computing -NEs using decentralized neural-network policies. Numerical experiments demonstrate that the proposed framework accommodates diverse traffic flow models and effectively captures collision avoidance, obstacle avoidance, and agent heterogeneity.

Paper Structure

This paper contains 14 sections, 3 theorems, 21 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Markov games for CAV control
  4. Problem Setup.
  5. Application to CAV Control.
  6. Collision Avoidance Beyond Mean-Field.
  7. Main Theoretical Results
  8. Policy gradient algorithm for $\alpha$-NE
  9. Numerical Experiments
  10. Interaction regimes in cost function
  11. Two-dimensional acceleration control with obstacles
  12. Heterogeneous vehicle types
  13. Conclusions
  14. Acknowledgement

Key Result

Proposition 3.1

Suppose that the game eq:state_i-eq:cost_i is an $\alpha$-potential game for some $\alpha\ge 0$, in the sense that there exists $\Phi:\pi\rightarrow {\mathbb R}$, called an $\alpha$-potential function, such that for all $i\in [N]$, $\phi_{-i}\in \pi_{-i}$, and $\phi_i,\phi'_i\in \pi_i$, Then for all $\epsilon\ge 0$, if $\bar{\phi}\in \pi$ satisfies $\Phi(\bar{\phi})\le \inf_{\phi\in \pi}\Phi(\phi

Figures (4)

  • Figure 1: Vehicle trajectories of the control-velocity model for $\beta=0$ (left) and $\beta=1$ (right)
  • Figure 2: Vehicle trajectories of the control-acceleration model for $\beta=0$ (left) and $\beta=1$ (right)
  • Figure 3: Vehicle trajectories under acceleration-control without obstacle (left), with a small obstacle (middle), and with a large obstacle (right)
  • Figure 4: Vehicle trajectories of different types under control-velocity (left) and control-acceleration (right)

Theorems & Definitions (7)

  • Definition 2.1
  • Proposition 3.1
  • Theorem 3.2
  • Remark 3.1
  • proof
  • Corollary 3.3
  • proof