Pith. sign in

REVIEW 4 major objections 5 minor 24 references

Hierarchical Game-Based Multi-Agent Decision-Making for Autonomous Vehicles

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper proposes a hierarchical game framework in which an autonomous vehicle selects a subset of surrounding traffic agents as game players through an interaction graph, reducing computational complexity from $2^N$ to $2^{N_h}$ while…

desk verdict The hierarchical player-selection idea is genuinely useful and the complexity reduction is sound, but Proposition 2's 'guaranteed safe' claim is a conditional tautology that assumes the interaction graph is correct for the whole horizon; the paper needs a final safety check or a receding-horizon guarantee. read the letter →

arxiv 2507.21941 v1 pith:NGZCYY6X submitted 2025-07-29 eess.SY cs.SY

Mushuang Liu , Yan Wan , Frank Lewis , Subramanya Nageshrao , H. Eric Tseng , Dimitar Filev This is my paper · ORCID
classification eess.SYcs.SY
keywords hierarchicalgameinteractiongraphautonomousdrivingmulti-agentdecision-makingNashequilibriumtime-to-collisionintersectioncrossingplayerselection
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to make game-theoretic decision-making for autonomous vehicles practical in dense traffic. Instead of playing a game with every agent in sight, the ego vehicle builds an interaction graph from trajectory conflicts and plays a normal-form game with only the first few levels of neighbors. The authors claim this reduces the computational cost from exponential in the total number of agents to exponential in a much smaller selected set, while a formal result (Proposition 2) guarantees the ego's decision remains safe. They further claim that this captures multi-agent correlations, so it avoids the unnecessary yielding that pairwise games produce. A branch-based decomposition into sub-games reduces the cost even more.

What carries the argument

The central machinery is the interaction graph, a level-structured map of directional dependence between agents. The ego's first-level neighbors are agents whose planned trajectories intersect its own, and the kth level is formed recursively from agents that conflict with the (k-1)th level. Trajectory-based conflicts define edges, so the graph directly encodes which agents can affect the ego's safety and which agents affect those agents. Two reductions shrink the graph: agent clustering merges agents with parallel trajectories into one group, and representative-agent selection chooses the member with minimal $|T^c_{ij}-T^c_{ji}|$ as the group's game player. The improved hierarchical game then decomposes the resulting game into sub-games along branches, splitting whenever two branches share no common agents.

What would settle it

Run the hierarchical game with well-designed payoffs in a scenario where a vehicle not in the selected player set (a second-level neighbor or an unselected agent) changes its planned trajectory and enters the ego's path during the current decision interval, before the next game round is computed; if the ego follows its game decision and a collision occurs, the assumption underlying Proposition 2 is violated.

Watch

Extended reading notes

Core claim

The central claim is that the ego's safety depends only on its first-level neighbors—those whose planned trajectories conflict with its own—so including at least these agents as game players is sufficient for a safe decision. With an interaction graph that groups agents into levels by trajectory conflicts, the ego plays a multi-player game with the first k levels, chosen to fit its real-time budget. The paper proves this hierarchical game yields a global Nash solution when all levels are included (Proposition 1) and guarantees safety even when only a subset is included (Proposition 2). Compared with pairwise games, the key discovery is efficiency: the hierarchical game sees that a first-level agent will yield to a second-level agent, and lets the ego proceed instead of waiting. An improved version decomposes the selected game into branch sub-games whenever branches share no common agents, further cutting computation.

Load-bearing premise

The safety guarantee in Proposition 2 rests on the assumption that the first-level neighbors—agents whose current planned trajectories conflict with the ego—are the only agents that can threaten the ego during the decision interval; if a second-level neighbor changes its trajectory or a prediction error misses a conflict, that agent can become a first-level threat before the next game round, and the proof no longer applies.

Editorial extensions

If this is right

  • In the reported simulations, the ego generates safe decisions in under 10 ms with 6 to 10 surrounding vehicles, making the approach real-time feasible.
  • The hierarchical game lets the ego proceed when a first-level agent is itself blocked by a second-level agent, avoiding the unnecessary yielding that pairwise games produce.
  • Computational complexity drops from $2^N$ for the full multi-player game to $2^{N_h}$ for the hierarchical game, and to $\sum_{j=1}^{M} 2^{N_j}$ with the branch decomposition.
  • Agent clustering collapses groups of parallel-moving agents (for example, several pedestrians) into one game player, so the ego only has to be safe against the most conflicting representative.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same first-level safety argument could extend beyond intersections to any scenario where trajectory conflicts define the interaction graph, such as unprotected turns, roundabouts, and merging lanes; the paper does not demonstrate these cases.
  • The branch-based sub-game decomposition suggests that independent branches could be solved on parallel compute units, an additional speedup the paper does not explicitly claim.
  • If prediction uncertainty is added, the safety guarantee will need a bound on how quickly a hidden conflict can become a first-level threat; the authors themselves list trajectory prediction as future work.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper proposes a hierarchical game-theoretic decision-making framework for autonomous vehicles at intersections. The ego vehicle constructs an interaction graph from predicted trajectories, defines levels of trajectory-conflict neighbors, and selects the first k levels as game players, with optional clustering of similar agents and a decomposition of the game into sub-games. The manuscript claims that this approach reduces computational complexity from 2^N to 2^Nh, yields more efficient decisions than pairwise games, and guarantees safety. Simulation studies are presented for three-vehicle and six-to-ten-vehicle intersection scenarios.

Significance. The complexity-reduction idea is straightforward and the counting argument is valid; focusing on interaction-relevant agents is intuitive, and the simulations suggest possible efficiency gains over pairwise games in selected scenarios. However, the central safety guarantee is not established: it rests on a definitional tautology, an unverified 'well-designed payoff' assumption, and the absence of a final safety check that appeared in the prior three-level framework. The improved hierarchical game's safety claim is likewise unproven. If the safety claims are properly qualified and supported (or replaced by a verifiable safety filter), the framework could be a useful contribution to real-time multi-agent decision-making; as written, the headline guarantee is not justified.

major comments (4)
  1. [Section III-C (Proposition 2)] The proof of Proposition 2 is a tautology: first-level neighbors are defined as the agents with trajectory conflicts (Definition 4), so the ego is 'guaranteed safe' only if the interaction graph correctly and completely identifies all conflict partners for the entire decision period. The graph is rebuilt every dt in Algorithm 1 from predicted trajectories, but the proof contains no receding-horizon argument and no bound on prediction error. A second-level agent can change its action and become a first-level threat before the next round, and a prediction error can miss a conflict; in both cases the conclusion no longer follows. Unlike the three-level framework reviewed in Section II-A, Algorithm 1 has no final safety check to catch such failures, so the central claim 'the ego's decision is still guaranteed to be safe' is not supported.
  2. [Section IV (Payoff design)] Proposition 2 assumes 'game payoffs are well-designed such that the Nash decision is a safe decision,' but the manuscript never proves this for the payoff functions in Section IV. The payoffs contain free parameters beta, theta1, theta2, theta3, theta4 (and reward R) that are said to be learned offline from reference [17], with no disclosure of parameter values or a verification argument that every Nash equilibrium of Equations (5)-(12) is safe. The safety guarantee thus reduces to an assumption that is essentially the desired conclusion.
  3. [Section III-D (Improved hierarchical game)] The improved hierarchical game is claimed to reduce complexity from 2^Nh to the sum over j of 2^Nj 'with guaranteed safety,' but no proposition or proof is given for the decomposition. Proposition 2 applies only to the original hierarchical game and does not cover the case where the game is split into branches and the most conservative decision is selected across sub-games. There is no demonstration that branch decomposition preserves the safety property when branches do not share common agents, nor an analysis of how interactions across branches affect the conservative selection.
  4. [Section V-B (Study 1)] The abrupt-change experiment shown in Figure 19 is reported only qualitatively, with a single screenshot sequence. No quantitative safety margin, minimum time-to-collision, or statistical evaluation across multiple runs is provided, so the results do not substantiate the claimed safety guarantee beyond the specific scenario and parameter choices.
minor comments (5)
  1. [Algorithm 1] The time variable in Line 1 is written as 'dT' while the Input block and surrounding text use 'dt'; these should be unified.
  2. [Section IV-A] Equations (8) and (9) use aN in the argument list of J_s_1, although the game has Nj players as defined at the beginning of Section IV. Use aNj or (a_1,...,a_Nj) consistently.
  3. [Section III-D] There is a typo: 'Brunch 2' should be 'Branch 2' in the paragraph after Definition 9.
  4. [Figure 18] The figure contains a stray '(a)' label in what appears to be a single-panel figure; this should be removed.
  5. [References] Reference [17] is cited as 'Submitted' and the payoff-learning method and the three-level framework with a final safety check are deferred to it. To make the safety analysis self-contained, the manuscript should either include the learned parameter values or summarize the learning architecture and validation results.

Circularity Check

2 steps flagged · score 6.0 of 10

The safety guarantee in Proposition 2 restates its own assumption that the Nash solution is safe for the included players, and the payoff parameters that would satisfy this assumption are fitted offline in prior work; the complexity and efficiency contributions remain independent.

  1. self definitional [Section III-C, Proposition 2 and its proof]
    "Assume that the game payoffs are well-designed such that the Nash decision is a safe decision for the game players considering the interactions captured by the game. Then even though only a subset of surrounding agents are included in the game player set, the ego's decision is still guaranteed to be safe. ... Proof: ... As the first level neighbors are the only agents (among all surrounding agents) that have trajectory conflicts with the ego, the ego is safe as long as the interactions with the first level neighbors are captured."

    The claimed guarantee is exactly the assumption: 'payoffs are well-designed such that the Nash decision is a safe decision' is the same as 'the Nash decision is safe.' The proof then adds only the definitional fact that first-level neighbors are the agents with trajectory conflicts (Definition 4). Thus Proposition 2 reduces to: if the payoffs make the Nash decision safe, then the decision is safe. It supplies no independent safety mechanism, no receding-horizon argument, and no prediction-error bound showing that agents outside the current first level cannot become conflicting before the next game round.

  2. fitted input called prediction [Section IV-B, final paragraph]
    "The constant parameters in payoffs, i.e., β, θ1, θ2, θ3, θ4, can be learned from offline supervised learning algorithms developed in [17]."

    Proposition 2's safety result depends entirely on the payoffs being 'well-designed' so that Nash solutions are safe. But the constants that make the payoffs well-designed are not derived or verified here; they are fitted offline by learning algorithms in the authors' prior work [17]. The simulations then demonstrate safe behavior under those fitted values, so the empirical 'verification' of the safety guarantee is a demonstration of the fitted input rather than an independent prediction. The load-bearing premise is delegated to a self-citation without disclosing the learned values or proving that they satisfy the proposition's hypothesis.

full rationale

The paper's independent contribution—selecting a subset of game players via an interaction graph to reduce complexity from 2^N to 2^Nh, and the simulation comparisons against pairwise games—does not itself reduce to an input. However, the central safety claim does. Proposition 2's conclusion ('ego's decision is still guaranteed to be safe') is a paraphrase of its own hypothesis ('payoffs are well-designed such that the Nash decision is a safe decision'), with the interaction graph contributing only the definitional observation that first-level neighbors are the agents whose predicted trajectories conflict with the ego. The offline-learned payoff constants in Section IV-B are the unverified fitted inputs on which this conditional safety rests. The paper also omits the final safety check present in the reviewed three-level framework [17] (Section II-A: 'the generalization of the first and third levels are straightforward'), replacing it with the 'well-designed payoffs' assumption in Proposition 2. Accordingly, the safety prediction partially reduces by construction, while the complexity and efficiency claims retain independent content.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central safety and efficiency claims rest on the interaction graph being complete and on payoff parameters being well designed; both are assumed rather than validated. The payoff constants are fitted offline, and the trajectory-prediction accuracy is assumed. No new physical entities are introduced.

free parameters (4)
  • beta = not specified
    Weight in payoff J_i = beta Js_i + (1-beta) Jr_i; tunes safety versus rule compliance; stated as learnable, no value given.
  • theta1, theta2, theta3, theta4 = not specified
    Constants in the safety-based payoff (Eqs. 8-9) that tune how TTC and TOSC are weighted; said to be learned offline in [17].
  • R = not specified
    Positive reward added to the safety payoff when a second-level neighbor is expected to go; value not given.
  • Nmax = e.g., 5, 6
    Maximum number of game players determined by computational budget; chosen per scenario.
assumptions (5)
  • domain assumption Nash equilibrium is the appropriate solution concept for traffic interactions.
    The framework selects Nash decisions; this assumes agents optimize their payoffs and that the equilibrium is a valid predictor of behavior.
  • domain assumption Future trajectories of all agents are known or accurately predicted for conflict detection.
    Algorithm 1 needs future trajectories to build the interaction graph; no uncertainty model is given.
  • ad hoc to paper Safety is equivalent to avoiding agents with trajectory conflicts, and first-level neighbors are the only such agents.
    Used in Proposition 2 to conclude safety from k>=1; ignores prediction errors and agents entering the conflict set later.
  • ad hoc to paper Payoffs are well designed so that the Nash decision is safe.
    Stated as an assumption in Proposition 2; the paper does not prove that the proposed payoff design satisfies this.
  • domain assumption Clustered agents with parallel trajectories can be represented by one 'most conflicting' agent.
    Definitions 6 and 8 assume safety w.r.t. the representative implies safety w.r.t. the group.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Hierarchical Game-Based Multi-Agent Decision-Making for Autonomous Vehicles." pith.science (2026). https://pith.science/paper/NGZCYY6X

@misc{pith2026250721941,
  author       = {Pith},
  title        = {Pith review of: Hierarchical Game-Based Multi-Agent Decision-Making for Autonomous Vehicles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NGZCYY6X}},
  note         = {Machine review of arXiv:2507.21941}
}
read the original abstract

This paper develops a game-theoretic decision-making framework for autonomous driving in multi-agent scenarios. A novel hierarchical game-based decision framework is developed for the ego vehicle. This framework features an interaction graph, which characterizes the interaction relationships between the ego and its surrounding traffic agents (including AVs, human driven vehicles, pedestrians, and bicycles, and others), and enables the ego to smartly select a limited number of agents as its game players. Compared to the standard multi-player games, where all surrounding agents are considered as game players, the hierarchical game significantly reduces the computational complexity. In addition, compared to pairwise games, the most popular approach in the literature, the hierarchical game promises more efficient decisions for the ego (in terms of less unnecessary waiting and yielding). To further reduce the computational cost, we then propose an improved hierarchical game, which decomposes the hierarchical game into a set of sub-games. Decision safety and efficiency are analyzed in both hierarchical games. Comprehensive simulation studies are conducted to verify the effectiveness of the proposed frameworks, with an intersection-crossing scenario as a case study.

Figures

Figures reproduced from arXiv: 2507.21941 by the authors.

Figure 2
Figure 2. The intersection-crossing scenario [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Normal-form game of intersection-crossing [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 1
Figure 1. Three-level decision-making framework Consider a four-way stop sign intersection shown in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Two-player normal-form game A payoff table, e.g., [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]
Figure 5
Figure 5. Figure 5: An intersection-crossing example with multiple agents [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 7
Figure 7. Figure 7: General interaction graph In addition to characterizing the interaction relationships, we notice that the clustering of agents is also important in determining the interaction graph to reduce the number of game players. Consider the intersection-crossing scenario shown…
Figure 8
Figure 8. Figure 8: Illustrative example to motivate agent clustering [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]
Figure 10
Figure 10. Figure 10: Time-to-collisions With the defined TTC, we propose the following represen￾tative agent selection criterion. Definition 8 (Representative agent selection). An agent j in the agent i’s first level of neighbors is selected as a represen￾tative agent of a clustered group…
Figure 9
Figure 9. Figure 9: Illustrative example to show the effectiveness of agent clustering [PITH_FULL_IMAGE:figures/full_fig_p005_9.png]
Figure 11
Figure 11. Figure 11: (a) Illustrative example for the comparison between hierarchical [PITH_FULL_IMAGE:figures/full_fig_p007_11.png]
Figure 13
Figure 13. Figure 13: Examples of interaction graphs with (a) three branches and (b) two [PITH_FULL_IMAGE:figures/full_fig_p007_13.png]
Figure 14
Figure 14. Figure 14: Definition of time-of-safe-crossing To design the safety-based payoff for the ego (i.e., J s 1 (a1, a2, · · · , aNj )), let us consider a two-level Nj -player game. We assume, without loss of generality, that agents {2, 3, · · · , m} are in the first level and agents …
Figure 15
Figure 15. Figure 15: With rule-based payoff only, the ego decides to go when (a) it comes [PITH_FULL_IMAGE:figures/full_fig_p009_15.png]
Figure 16
Figure 16. Figure 16: (a) The ego crashes into vehicle 2 when vehicle 2 violates the traffic [PITH_FULL_IMAGE:figures/full_fig_p009_16.png]
Figure 19
Figure 19. Figure 19: The ego’s decision in Study 1. (a) The ego crosses the intersection in [PITH_FULL_IMAGE:figures/full_fig_p010_19.png]
Figure 20
Figure 20. Figure 20: The ego performs well in various scenarios. [PITH_FULL_IMAGE:figures/full_fig_p010_20.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

  1. [17]

    A three-level game-theoretic decision-making framework for autonomous vehicles,

    M. Liu, Y . Wan, S. Lewis, Frank Nageshrao, and D. Filev, “A three-level game-theoretic decision-making framework for autonomous vehicles,” Submitted to IEEE Transactions on Intelligent Transportation Systems , 2021

    work page 2021

  2. [1]

    Environmental, safety legal and societal implications of autonomous driving systems,

    A. Eugensson, M. Br ¨annstr¨om, D. Frasher, M. Rothoff, S. Solyom, and A. Robertsson, “Environmental, safety legal and societal implications of autonomous driving systems,” in International Technical Conference on the Enhanced Safety of Vehicles (ESV). Seoul, South Korea , 2013

    work page 2013

  3. [2]

    Set-based prediction of traffic participants on arbitrary road networks,

    M. Althoff and S. Magdici, “Set-based prediction of traffic participants on arbitrary road networks,” IEEE Transactions on Intelligent Vehicles , vol. 1, no. 2, pp. 187–202, 2016

    work page 2016

  4. [3]

    Stochastic model predictive control with a safety guarantee for automated driving,

    T. Br ¨udigam, M. Olbrich, D. Wollherr, and M. Leibold, “Stochastic model predictive control with a safety guarantee for automated driving,” IEEE Transactions on Intelligent Vehicles , 2021. 11

    work page 2021

  5. [4]

    Combining planning and deep reinforcement learning in tactical decision making for autonomous driving,

    C.-J. Hoel, K. Driggs-Campbell, K. Wolff, L. Laine, and M. J. Kochen- derfer, “Combining planning and deep reinforcement learning in tactical decision making for autonomous driving,” IEEE Transactions on Intel- ligent Vehicles, vol. 5, no. 2, pp. 294–305, 2019

    work page 2019

  6. [5]

    Human-like decision making for autonomous driving: A noncooperative game theoretic ap- proach,

    P. Hang, C. Lv, Y . Xing, C. Huang, and Z. Hu, “Human-like decision making for autonomous driving: A noncooperative game theoretic ap- proach,” IEEE Transactions on Intelligent Transportation Systems, 2020

    work page 2020

  7. [6]

    Interactive trajectory prediction of surrounding road users for autonomous driving using structural-lstm network,

    L. Hou, L. Xin, S. E. Li, B. Cheng, and W. Wang, “Interactive trajectory prediction of surrounding road users for autonomous driving using structural-lstm network,” IEEE Transactions on Intelligent Transporta- tion Systems, vol. 21, no. 11, pp. 4615–4625, 2019

    work page 2019

  8. [7]

    Autonomous vehicles that interact with pedestrians: A survey of theory and practice,

    A. Rasouli and J. K. Tsotsos, “Autonomous vehicles that interact with pedestrians: A survey of theory and practice,” IEEE transactions on intelligent transportation systems , vol. 21, no. 3, pp. 900–918, 2019

    work page 2019

Show all 24 references
  1. [8]

    A nash q- learning based motion decision algorithm with considering interaction to traffic participants,

    C. Xu, W. Zhao, L. Li, Q. Chen, D. Kuang, and J. Zhou, “A nash q- learning based motion decision algorithm with considering interaction to traffic participants,”IEEE Transactions on Vehicular Technology, vol. 69, no. 11, pp. 12 621–12 634, 2020

    2020

  2. [9]

    A merging–giveway interaction model of cars in a merging section: a game theoretic analysis,

    H. Kita, “A merging–giveway interaction model of cars in a merging section: a game theoretic analysis,” Transportation Research Part A: Policy and Practice, vol. 33, no. 3-4, pp. 305–312, 1999

    1999

  3. [10]

    Game- theoretic modeling of multi-vehicle interactions at uncontrolled intersec- tions,

    N. Li, Y . Yao, I. Kolmanovsky, E. Atkins, and A. R. Girard, “Game- theoretic modeling of multi-vehicle interactions at uncontrolled intersec- tions,” IEEE Transactions on Intelligent Transportation Systems , 2020

    2020

  4. [11]

    A game theoretic model predictive controller with aggres- siveness estimation for mandatory lane change,

    Q. Zhang, R. Langari, H. E. Tseng, D. Filev, S. Szwabowski, and S. Coskun, “A game theoretic model predictive controller with aggres- siveness estimation for mandatory lane change,” IEEE Transactions on Intelligent Vehicles, vol. 5, no. 1, pp. 75–89, 2019

    2019

  5. [12]

    A noncooperative game approach to au- tonomous racing,

    A. Liniger and J. Lygeros, “A noncooperative game approach to au- tonomous racing,” IEEE Transactions on Control Systems Technology , vol. 28, no. 3, pp. 884–897, 2019

    2019

  6. [13]

    Multi-vehicle automated driving as a generalized mixed-integer potential game,

    F. Fabiani and S. Grammatico, “Multi-vehicle automated driving as a generalized mixed-integer potential game,” IEEE Transactions on Intelligent Transportation Systems, vol. 21, no. 3, pp. 1064–1073, 2019

    2019

  7. [14]

    Enabling courteous vehicle interactions through game-based and dynamics-aware intent inference,

    Y . Wang, Y . Ren, S. Elliott, and W. Zhang, “Enabling courteous vehicle interactions through game-based and dynamics-aware intent inference,” IEEE Transactions on Intelligent Vehicles , vol. 5, no. 2, pp. 217–228, 2019

    2019

  8. [15]

    Game theoretic modeling of driver and vehicle interactions for verification and validation of autonomous vehicle control systems,

    N. Li, D. W. Oyler, M. Zhang, Y . Yildiz, I. Kolmanovsky, and A. R. Girard, “Game theoretic modeling of driver and vehicle interactions for verification and validation of autonomous vehicle control systems,”IEEE Transactions on control systems technology , vol. 26, no. 5, pp. ...

    2017

  9. [16]

    Game-theoretic lane-changing decision making and payoff learning for autonomous vehicles,

    V . Lopez, F. Lewis, M. Liu, Y . Wan, S. Nageshrao, and D. Filev, “Game-theoretic lane-changing decision making and payoff learning for autonomous vehicles,” submitted to IEEE Transactions on Vehicle Technology, 2020

    2020

  10. [18]

    Shoham and K

    Y . Shoham and K. Leyton-Brown, Multiagent systems: Algorithmic, game-theoretic, and logical foundations . Cambridge University Press, 2008

    2008

  11. [19]

    Decision making in multiagent systems: A survey,

    Y . Rizk, M. Awad, and E. W. Tunstel, “Decision making in multiagent systems: A survey,” IEEE Transactions on Cognitive and Developmental Systems, vol. 10, no. 3, pp. 514–529, 2018

    2018

  12. [20]

    Trajectory clustering: a partition- and-group framework,

    J.-G. Lee, J. Han, and K.-Y . Whang, “Trajectory clustering: a partition- and-group framework,” in Proceedings of the 2007 ACM SIGMOD international conference on Management of data , 2007, pp. 593–604

    2007

  13. [21]

    Similarity based vehicle trajectory clustering and anomaly detection,

    Z. Fu, W. Hu, and T. Tan, “Similarity based vehicle trajectory clustering and anomaly detection,” in Proceedings of IEEE International Confer- ence on Image Processing , vol. 2, 2005, pp. II–602

    2005

  14. [22]

    Kinematic and dynamic vehicle models for autonomous driving control design,

    J. Kong, M. Pfeiffer, G. Schildbach, and F. Borrelli, “Kinematic and dynamic vehicle models for autonomous driving control design,” in Proceedings of IEEE Intelligent Vehicles Symposium (IV) , 2015, pp. 1094–1099. Mushuang Liu is currently a Postdoctoral Research Fellow in the...

    2015

  15. [2016]

    Prior to that he worked as a post-doctoral research scholar at University of Michigan Ann-Arbor

    He is currently a Research Engineer at Ford Green Field Labs, Palo Alto, California. Prior to that he worked as a post-doctoral research scholar at University of Michigan Ann-Arbor. He is actively leveraging machine learning methods particularly reinforcement learning techniqu...

    1986

  16. [2020]

    Her research interests include decision-making in multi-agent systems, optimal control, distributed control, multi-player games, reinforcement learning, and their applications to UA V traffic man- agement, UA V networking, and autonomous driving. Her research has led to over 2...

    2008

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.