Trust-Aware Embodied Bayesian Persuasion

• The paper introduces TA-EBP, a framework that replaces manipulative tactics with transparent, trust-aware embodied signals to safely influence human-driven vehicles.
• It integrates Bayesian persuasion with a trust parameter and optimal forward nudge design, ensuring the human driver's belief update favors cautious behavior.
• Simulation results demonstrate that TA-EBP can eliminate collisions while significantly improving safe driving responses compared to baseline strategies.

Trust-Aware Embodied Bayesian Persuasion (TA-EBP) is a transparent, signal-commitment framework for safe and efficient AV–HV interaction at traffic intersections. It replaces manipulative or unpredictability-based influence with a principled, public signaling policy that accounts for human trust and grounds abstract signals in physically meaningful vehicle motions. In the formulation introduced in "Trust-Aware Embodied Bayesian Persuasion for Mixed-Autonomy" (Peng et al., 18 Sep 2025), the autonomous vehicle is the informed sender, the human-driven vehicle is the receiver, and persuasion is realized through a committed signaling scheme whose embodied form is an AV forward nudge. The framework is presented as a transparent and non-strategic alternative to traditional game-theoretic models, with the stated goals of enhancing both safety and efficiency while mitigating long-term trust erosion.

1. Problem formulation and interaction structure

TA-EBP studies an autonomous vehicle and a human-driven vehicle arriving at a two-way stop intersection. The AV privately knows its intent, either to proceed or to wait, while the HV observes the AV’s signal, updates her belief about the AV’s intent, and chooses how to drive. The timeline follows the classical commitment sequence: the AV publicly commits to a signaling scheme before the state is realized; nature draws the state; the AV sends a signal per the committed policy; the HV observes it, updates her belief, and takes an action (Peng et al., 18 Sep 2025).

The state space is $\Omega=\{\text{Go},\text{Stop}\}$ with common prior $p_0(\text{Go})=\lambda$ and $p_0(\text{Stop})=1-\lambda$. The HV action set is $$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$. The signal space is embodied: the AV emits a forward nudge of magnitude $s\ge 0$, or $s=0$ to remain stationary. The safety–efficiency tradeoff is asymmetric. Driving recklessly is efficient if the AV intends to Stop, but risky or catastrophic if the AV intends to Go. By contrast, DC is always safe but may be inefficient.

The utility specification is correspondingly explicit. If $\omega=\text{Go}$ and the HV chooses DR, the HV utility is $-r$ with $r>1$. If $\omega=\text{Stop}$ and the HV chooses DR, the HV utility is $p_0(\text{Go})=\lambda$0. If the HV chooses DC, the utility is $p_0(\text{Go})=\lambda$1 when $p_0(\text{Go})=\lambda$2 and $p_0(\text{Go})=\lambda$3 when $p_0(\text{Go})=\lambda$4. The AV utility is safety-oriented: $p_0(\text{Go})=\lambda$5 if the HV chooses DC and $p_0(\text{Go})=\lambda$6 if the HV chooses DR, irrespective of $p_0(\text{Go})=\lambda$7. This gives TA-EBP a sender objective that is explicitly aligned with inducing cautious behavior rather than maximizing passage priority.

2. Bayesian persuasion formalization

TA-EBP leverages Bayesian persuasion with sender, receiver, latent state, and embodied signal. The AV commits to a signaling scheme $p_0(\text{Go})=\lambda$8, the likelihood of emitting signal $p_0(\text{Go})=\lambda$9 in state $p_0(\text{Stop})=1-\lambda$0. The HV updates her belief by Bayes’ rule and best-responds by maximizing expected utility (Peng et al., 18 Sep 2025):

$p_0(\text{Stop})=1-\lambda$1

$p_0(\text{Stop})=1-\lambda$2

$p_0(\text{Stop})=1-\lambda$3

The expected utility under belief $p_0(\text{Stop})=1-\lambda$4 is

$p_0(\text{Stop})=1-\lambda$5

Within this formulation, the sender chooses $p_0(\text{Stop})=1-\lambda$6 to maximize expected $p_0(\text{Stop})=1-\lambda$7 subject to the receiver’s Bayesian best response. The commitment requirement is central: the AV commits to a public $p_0(\text{Stop})=1-\lambda$8 before $p_0(\text{Stop})=1-\lambda$9 is realized, ensuring transparency, and designs $$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$0 to optimally raise the HV posterior above the indifference threshold where DC is preferred or at least as good as DR.

Compared to prior Bayesian persuasion work, the framework explicitly introduces human trust into the posterior update and grounds the signals in continuous, physically realizable nudges. It assumes discrete states and actions, while signals are continuous but are embedded into a two-signal policy $$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$1 once optimality is derived. This suggests that the formal model preserves the tractability of low-dimensional persuasion while treating physical motion as the actual communication channel.

3. Trust-aware belief updating and the minimum persuadable trust level

A defining feature of TA-EBP is the trust parameter $$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$2, which interpolates between ignoring the signal and fully Bayesian updating. The trust-aware posterior is (Peng et al., 18 Sep 2025)

$$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$3

with

$$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$4

This convex combination captures the degree to which the HV incorporates the AV’s signal into her beliefs. At $$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$5, the receiver ignores the signal; at $$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$6, she performs fully trusting Bayesian updating.

The paper provides a general trust threshold theorem:

$$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$7

The theorem states that for any persuasion setting with trust $$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$8, sender, and receiver with default optimal action $$\mathcal A=\{\text{Drive Recklessly (DR)},\text{Drive if Clear (DC)}\}$$9, there exists a minimum persuadable trust $s\ge 0$0 such that, if $s\ge 0$1, no signaling scheme can persuade the receiver to select any action other than $s\ge 0$2. In the AV–HV setting, this formalizes “when to signal” by identifying the minimum trust needed to move the receiver from a default action.

For the two-state, two-action case, the threshold simplifies to

$s\ge 0$3

With $s\ge 0$4, $s\ge 0$5, $s\ge 0$6, and $s\ge 0$7, this yields

$s\ge 0$8

The reported sensitivities are

$s\ge 0$9

Both partial derivatives are negative for $s=0$0 and $s=0$1. The stated interpretation is that stronger prior that AV will Stop, or lower collision cost, raises the trust threshold required to persuade. A plausible implication is that trust calibration is not merely an auxiliary human-factor variable but a structural feasibility condition for influence.

4. Embodied signaling and the optimal forward nudge

TA-EBP grounds the abstract signal of persuasion theory into a continuous action: a forward nudge of magnitude $s=0$2. The HV’s intuitive likelihood model is monotonic: $s=0$3 increases with $s=0$4, while $s=0$5 decreases. Let

$s=0$6

The trust-aware posterior over Go as a function of $s=0$7 is (Peng et al., 18 Sep 2025)

$s=0$8

Because $s=0$9 is increasing in $\omega=\text{Go}$0, $\omega=\text{Go}$1 is strictly increasing in $\omega=\text{Go}$2. The design problem is therefore to choose the smallest effective nudge $\omega=\text{Go}$3 that crosses the persuasion boundary where the HV is indifferent between DR and DC.

The posterior threshold $\omega=\text{Go}$4 is defined by equating expected utilities:

$\omega=\text{Go}$5

Using the utilities of the intersection game, the threshold becomes

$\omega=\text{Go}$6

The optimization problem is to minimize $\omega=\text{Go}$7 subject to $\omega=\text{Go}$8, with $\omega=\text{Go}$9 and $-r$0 increasing. At the boundary $-r$1, the optimal nudge magnitude is

$-r$2

The paper terms this the optimal signal theorem: the minimum embodied signal $-r$3 required to persuade an HV with trust $-r$4.

An identity links the trust threshold and the persuasion boundary:

$-r$5

with $-r$6. It expresses that at minimal trust $-r$7, only a maximally informative signal achieves the persuasion boundary $-r$8; for $-r$9, $r>1$0 is unattainable irrespective of $r>1$1. This suggests that embodiment is not appended after the persuasion analysis; it is the mechanism through which informativeness becomes physically realizable.

5. Control policy and simulation evidence

The framework synthesizes the trust theorem and the optimal-signal theorem into a real-time policy with public commitment (Peng et al., 18 Sep 2025). Step 1 is to compute $r>1$2 and verify persuadability. If $r>1$3, persuasion is not attempted and the AV reverts to a default safe policy such as yielding. If $r>1$4, the AV proceeds to construct the signaling scheme. Step 2 forms $r>1$5 with $r>1$6 from the optimal signal theorem. The design sets $r>1$7 and $r>1$8, chooses $r>1$9, and calibrates $\omega=\text{Stop}$0 to make $\omega=\text{Stop}$1 exactly persuasive by enforcing $\omega=\text{Stop}$2. This yields

$\omega=\text{Stop}$3

and therefore

$\omega=\text{Stop}$4

Step 3 is commitment and execution:

$\omega=\text{Stop}$5

$\omega=\text{Stop}$6

The total probability of emitting $\omega=\text{Stop}$7 is

$\omega=\text{Stop}$8

which is also the fraction of AV–HV interactions that result in the safe DC response, and is stated to be strictly higher than the fully revealing policy’s $\omega=\text{Stop}$9.

The mixed-autonomy environment is a single-lane figure-8 track with a 2-way stop intersection. Eight AVs and eight HVs circulate. Encounters at the intersection trigger the AV strategy; identical-type pairs cross by arrival order. Vehicles cruise at $p_0(\text{Go})=\lambda$00 units/s, maintain at least $p_0(\text{Go})=\lambda$01 units following distance, and stop $p_0(\text{Go})=\lambda$02 units from the intersection center. Collisions only occur at the intersection if both proceed simultaneously. The simulation uses $p_0(\text{Go})=\lambda$03, collision penalty $p_0(\text{Go})=\lambda$04, trust $p_0(\text{Go})=\lambda$05, and intuitive likelihoods on $p_0(\text{Go})=\lambda$06 given by $p_0(\text{Go})=\lambda$07 and $p_0(\text{Go})=\lambda$08, so $p_0(\text{Go})=\lambda$09.

Three strategies are compared over one-hour simulation using collision rate and DC rate. In "No EBP," the AV never nudges; collisions are $p_0(\text{Go})=\lambda$10 and DC rate is $p_0(\text{Go})=\lambda$11, but AVs perpetually yield and throughput is near zero when paired with HVs. In "No Trust," the AV computes the signal assuming full trust $p_0(\text{Go})=\lambda$12, while the HV updates with true $p_0(\text{Go})=\lambda$13; collisions are $p_0(\text{Go})=\lambda$14 and DC rate is $p_0(\text{Go})=\lambda$15. In TA-EBP, the calibrated nudge is $p_0(\text{Go})=\lambda$16, collisions are $p_0(\text{Go})=\lambda$17, and DC rate is $p_0(\text{Go})=\lambda$18. The paper reports that this is consistent with the theoretical $p_0(\text{Go})=\lambda$19 rate and eliminates collisions while improving traffic flow compared to baselines that either ignore trust or lack communication.

6. Relation to adjacent research traditions

TA-EBP is situated at the intersection of Bayesian persuasion, trust-aware human–robot interaction, and mixed-autonomy control. The paper explicitly states that it builds on Bayesian persuasion, for example the work associated with Kamenica and Gentzkow, but adapts it to embodied human–robot interaction by introducing trust-aware posterior updates, grounding signals in continuous physical actions with a derived optimal magnitude, and committing to a transparent signaling scheme rather than optimizing myopic strategic actions as in Stackelberg game-theoretic models (Peng et al., 18 Sep 2025).

A related line of work appears in "Approximating Human Models During Argumentation-based Dialogues" (Tang et al., 2024). There, an agent maintains a probability distribution $p_0(\text{Go})=\lambda$20 over possible human models, updates it through Bayesian inference over an argument trace, and uses trust-based and certainty-based update mechanisms. Trust in agent arguments is linked to subjective probability through a prospect-theoretic weighting function inspired by Tversky–Kahneman, while human certainty is mapped directly into probabilities. TA-EBP is described there as extending this probabilistic human-modeling perspective to a sender–receiver persuasion setting with embodied Human–Robot Interaction. This suggests a broader interpretation of TA-EBP in which “trust-aware” refers not only to a scalar credibility parameter at an intersection, but to a family of mechanisms for belief shaping under explicit human uncertainty.

"Clustering Trust Dynamics in a Human-Robot Sequential Decision-Making Task" (Bhat et al., 2022) provides a different but complementary trust-aware formalism. That work models trust as a Beta-distributed state in a finite-horizon MDP, updates it based on success and failure, and reports three trust-dynamics clusters: Bayesian decision makers, oscillators, and disbelievers. TA-EBP is not formulated there as a theorem-driven persuasion model, but the paper identifies trust as a strong driver of compliance and suggests personalization based on trust dynamics and individual differences.

"Bayesian Persuasive Driving" (Peng et al., 2018) supplies a prior embodied driving formulation in which the ego vehicle is the persuader and the surrounding vehicle is the persuadee. In that model, signals are motion states, beliefs and posteriors are Gaussian, and the sender chooses a signaling distribution to shape the receiver’s posterior about a latent world state. The same source explicitly notes that trust is not modeled as a dynamic state and proposes trust-aware insertion points through reliability-adjusted covariances. TA-EBP departs from that architecture by making trust an explicit posterior-interpolation parameter and by deriving a minimum trust level required for influence.

A different trust formalization appears in "Informativeness and Trust in Bayesian Persuasion" (Deori et al., 2024), which characterizes Stackelberg game value and informativeness through linear programs subject to trust constraints. Those constraints require that any signal in a persuasion strategy contain more truth than untruth. TA-EBP does not use that linear-programming framework, but the connection is conceptually direct: both approaches treat trust as a formal restriction on obfuscation rather than a purely behavioral outcome.

7. Assumptions, limitations, ethics, and scope of generalization

The stated assumptions of TA-EBP are narrow and explicit. The trust parameter is static and known per interaction. Utilities and the prior are shared knowledge. Rationality is idealized but modulated by $p_0(\text{Go})=\lambda$21. Signals are observable, and commitment is credible. Potential failure cases include extreme low trust $p_0(\text{Go})=\lambda$22 and mis-specified human intuitive likelihoods (Peng et al., 18 Sep 2025).

The ethical position of the framework is defined in terms of public commitment and calibrated signaling. The AV commits ex ante to a public, credible signaling scheme; the HV knows the AV’s utility and policy; and signals are calibrated to just reach indifference, minimizing unnecessary assertiveness. The paper therefore contrasts TA-EBP with manipulative or overly assertive strategies that rely on strategic opacity, randomness, or unpredictability and that can erode trust over repeated interactions. Within the scope of the reported formulation, persuasion is presented as transparent rather than deceptive.

The reported generalization claim is also bounded. The framework is said to extend beyond traffic intersections to other HRI scenarios where embodied signals, such as robot arm pre-movements, can safely and transparently shape human beliefs and actions. This suggests transfer at the level of sender–receiver structure and embodied signaling rather than immediate transfer of the specific two-state, two-action utility model.

Reproducibility is unusually explicit. The simulator is a custom figure-8 track with the stated vehicle speed, following-distance, and stopping-distance parameters; the priors, collision penalty, trust value, and intuitive likelihoods are all specified; and the baselines are defined operationally. The paper states that these details, together with the equations above, suffice to replicate the reported results. For arXiv-oriented readers, the main significance of TA-EBP is therefore not only the intersection application, but the combination of public commitment, trust-threshold analysis, and embodied signal design within a single persuasion framework.