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arxiv: 2604.20231 · v1 · submitted 2026-04-22 · 💻 cs.RO

Toward Cooperative Driving in Mixed Traffic: An Adaptive Potential Game-Based Approach with Field Test Verification

Shiyu Fang , Xiaocong Zhao , Xuekai Liu , Peng Hang , Jianqiang Wang , Yunpeng Wang , Jian Sun This is my paper

Pith reviewed 2026-05-10 00:52 UTC · model grok-4.3

classification 💻 cs.RO
keywords cooperative drivingmixed trafficpotential gameShapley valueautonomous vehicleshuman-driven vehiclesadaptive estimationfield test
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The pith

An adaptive potential game framework lets autonomous vehicles cooperate with human drivers by aligning individual goals with system safety and efficiency while refining preference estimates from observed behavior.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces an adaptive potential game approach for mixed traffic where autonomous and human-driven vehicles share the road. It defines a system utility from individual utilities via a monotonic link, allowing joint optimization of personal and collective outcomes. Shapley values quantify each vehicle's marginal contribution, and human driver preferences are updated dynamically by matching real actions against the model's estimates. Ablation and comparative tests show gains in cooperation rates, safety, and efficiency. Field experiments confirm the method works on actual roads.

Core claim

The adaptive potential game (APG) establishes a system utility function from the general form of individual utilities and their monotonic relationship to system objectives. It applies the Shapley value to compute each vehicle's marginal utility and refines HDV preference estimates in real time by comparing observed behavior to APG-predicted actions, yielding measurable improvements in mixed-traffic safety and efficiency.

What carries the argument

Adaptive potential game (APG) that uses monotonic individual-to-system utility mapping, Shapley-value marginal contribution calculation, and online comparison of observed HDV actions to estimated actions for preference refinement.

If this is right

  • Individual vehicle objectives and global traffic safety and efficiency can be optimized at the same time.
  • Shapley-value weighting lets each vehicle's contribution to cooperation be quantified and used in decision-making.
  • Continuous preference refinement raises the rate at which cooperative maneuvers succeed in mixed fleets.
  • The same structure supports real-time deployment, as shown by successful field tests on public roads.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework could be tested in denser urban intersections or on highways with frequent lane changes to check whether the monotonicity assumption still holds under higher interaction density.
  • Integration with existing perception modules would allow the preference estimator to run on raw sensor data rather than requiring perfect state information.
  • If the preference update rule proves stable across different driver populations, the method could be transferred to regions with distinct driving cultures without full retraining.

Load-bearing premise

A monotonic relationship holds between each vehicle's individual utility and overall system objectives, and observed human driver behavior can be compared reliably to the model's estimated actions to refine preferences.

What would settle it

A controlled field test in which the APG method produces no measurable gain in collision-avoidance rates or average travel time compared with a non-adaptive game baseline when human preferences are updated from observed actions.

Figures

Figures reproduced from arXiv: 2604.20231 by Jianqiang Wang, Jian Sun, Peng Hang, Shiyu Fang, Xiaocong Zhao, Xuekai Liu, Yunpeng Wang.

Figure 1
Figure 1. Figure 1: Challenges of cooperative driving under mixed-traffic conditions. A) Conflicts between individual [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the proposed APG cooperative driving framework. A) Equilibrium-secured system [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Vehicle trajectories without adaptive weight updates. [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Vehicle trajectories, speeds, and accelerations with adaptive weight updates. [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Rates of success of different methods with various rates of penetration. [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: presents the PET distributions for the different methods. Overall, the proposed APG framework maintains relatively large PET values, indicating a high margin of safety during interactions. The numbers shown in the figure denote the proportion of high-risk events excluding collisions. Specifically, our APG method results in only 1.4% of high-risk events, which is slightly higher than the 1.3% associated wit… view at source ↗
Figure 7
Figure 7. Figure 7: Average delay performance of different methods with various rates of penetration. [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: By mapping APG-driven real-field CAVs and virtual HDVs into the same digital [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 8
Figure 8. Figure 8: Workflow of the virtual-reality testing system. [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Vehicle trajectories and performance analysis controlled by a commercial algorithm. [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Vehicle trajectories and performance analysis controlled by the proposed APG framework. [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
read the original abstract

Connected autonomous vehicles (CAVs), which represent a significant advancement in autonomous driving technology, have the potential to greatly increase traffic safety and efficiency through cooperative decision-making. However, existing methods often overlook the individual needs and heterogeneity of cooperative participants, making it difficult to transfer them to environments where they coexist with human-driven vehicles (HDVs).To address this challenge, this paper proposes an adaptive potential game (APG) cooperative driving framework. First, the system utility function is established on the basis of a general form of individual utility and its monotonic relationship, allowing for the simultaneous optimization of both individual and system objectives. Second, the Shapley value is introduced to compute each vehicle's marginal utility within the system, allowing its varying impact to be quantified. Finally, the HDV preference estimation is dynamically refined by continuously comparing the observed HDV behavior with the APG's estimated actions, leading to improvements in overall system safety and efficiency. Ablation studies demonstrate that adaptively updating Shapley values and HDV preference estimation significantly improve cooperation success rates in mixed traffic. Comparative experiments further highlight the APG's advantages in terms of safety and efficiency over other cooperative methods. Moreover, the applicability of the approach to real-world scenarios was validated through field tests.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes an adaptive potential game (APG) framework for cooperative decision-making among connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs) in mixed traffic. It defines a system utility function from individual utilities via a claimed monotonic relationship to enable joint optimization, incorporates Shapley values to quantify each vehicle's marginal contribution, and dynamically refines HDV preference estimates online by comparing observed trajectories against actions computed by the current APG model. Ablation studies, comparative simulations, and field tests are presented to claim improvements in safety and efficiency metrics over baselines.

Significance. If the central claims hold, the work offers a practical extension of potential games to heterogeneous mixed-traffic settings, with explicit handling of HDV variability through online adaptation. The inclusion of field-test verification and ablation results demonstrating benefits from adaptive Shapley-value and preference updates are concrete strengths that distinguish it from purely simulation-based game-theoretic approaches. Successful validation could inform deployable CAV coordination algorithms that respect individual vehicle objectives while improving system-level outcomes.

major comments (2)
  1. [§4.2] §4.2 (HDV Preference Refinement): The online update compares observed HDV trajectories to actions selected by the current APG model and treats the latter as reference for preference correction. This step is load-bearing for the adaptivity claim, yet no convergence proof, Lyapunov-style stability argument, or sensitivity analysis under realistic sensor noise or initial preference mismatch is supplied; the risk of error reinforcement noted in the skeptic's analysis therefore remains unaddressed.
  2. [§3.1] §3.1 (System Utility Construction): The assertion that a monotonic mapping between individual utilities and system utility permits simultaneous optimization is central to the joint-optimization guarantee, but the manuscript provides neither an explicit functional form for the monotonicity nor a proof that the Shapley-value allocation preserves the claimed monotonicity under the heterogeneous utility functions used for HDVs.
minor comments (2)
  1. [Table 2, Figure 5] Table 2 and Figure 5: error bars or standard deviations are omitted from the reported safety and efficiency metrics, making it difficult to assess statistical significance of the claimed improvements over baselines.
  2. [§3.3] Notation: the symbol for the adaptive preference vector is introduced without an explicit update equation; readers must infer the precise recursion from surrounding prose.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the theoretical and practical aspects of our adaptive potential game framework. We address each major comment below and outline the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: [§4.2] §4.2 (HDV Preference Refinement): The online update compares observed HDV trajectories to actions selected by the current APG model and treats the latter as reference for preference correction. This step is load-bearing for the adaptivity claim, yet no convergence proof, Lyapunov-style stability argument, or sensitivity analysis under realistic sensor noise or initial preference mismatch is supplied; the risk of error reinforcement noted in the skeptic's analysis therefore remains unaddressed.

    Authors: We acknowledge that the manuscript lacks a formal convergence proof or Lyapunov-style stability analysis for the HDV preference refinement. The update rule is presented as a practical online mechanism whose benefits are shown empirically via ablation studies, comparative simulations, and field tests. To directly address robustness concerns, including sensor noise and potential error reinforcement, we will add a dedicated sensitivity analysis section with new simulation results under noisy observations and varying initial preference mismatches. This empirical strengthening will be included in the revision, while noting that a complete theoretical guarantee remains an open direction for future work. revision: partial

  2. Referee: [§3.1] §3.1 (System Utility Construction): The assertion that a monotonic mapping between individual utilities and system utility permits simultaneous optimization is central to the joint-optimization guarantee, but the manuscript provides neither an explicit functional form for the monotonicity nor a proof that the Shapley-value allocation preserves the claimed monotonicity under the heterogeneous utility functions used for HDVs.

    Authors: Section 3.1 defines the system utility via a general monotonic relationship to the aggregate of individual utilities, enabling the claimed joint optimization. We agree that an explicit functional form and a demonstration that Shapley-value marginal contributions preserve monotonicity for heterogeneous HDV utilities would improve rigor. In the revised manuscript we will specify the exact transformation employed (a scaled sum that maintains monotonicity) and include a short proof sketch showing that the Shapley allocation inherits the monotonic property under the utility heterogeneity considered. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the APG derivation chain

full rationale

The paper constructs the system utility from a general individual utility via an explicit monotonic relationship, which is the standard definition enabling potential-game equivalence rather than a self-referential loop. Shapley values are invoked as an external cooperative-game tool to quantify marginal contributions. The HDV preference update compares observed trajectories against current APG actions in an online refinement loop; this is an iterative estimator, not a definitional reduction where the 'prediction' is forced to equal the fitted input by construction. Ablation studies, comparative experiments, and field-test validation supply independent empirical checks outside the derivation. No quoted equation or step reduces the claimed output to the input tautologically.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Based solely on the abstract, the central claim rests on the existence of a monotonic relationship between individual and system utilities and the feasibility of dynamic HDV preference estimation. No explicit free parameters are named. The APG itself functions as the primary invented construct.

axioms (1)
  • domain assumption A monotonic relationship exists between individual utility and system utility that allows simultaneous optimization of both.
    Explicitly stated as the basis for establishing the system utility function.
invented entities (1)
  • Adaptive Potential Game (APG) framework no independent evidence
    purpose: To enable cooperative driving in mixed CAV-HDV traffic by quantifying marginal utilities via Shapley values and refining HDV preferences online.
    Introduced as the core contribution; independent evidence is limited to the paper's own ablation and field-test claims.

pith-pipeline@v0.9.0 · 5537 in / 1447 out tokens · 43398 ms · 2026-05-10T00:52:59.083847+00:00 · methodology

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