The Dynamic Verifiable Multi-Agent Human Agentic Loyalty Loop (DVM-HALL) Model and the Net Human-Agent Score (NHAS) in Autonomous Commerce¶

🕒 Published (v1): 2026-07-15 16:27 UTC · Source: Arxiv · link

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TL;DR¶

This paper introduces DVM-HALL, a mathematical framework that reconceptualizes brand loyalty in markets where AI agents execute purchasing decisions on behalf of humans. It formalizes brand selection as a softmax over a composite utility blending human emotional equity and agentic machine-experience utility, weighted by dynamic trust and delegation coefficients. It also proposes NHAS (Net Human-Agent Score), an auditable alignment metric intended to replace NPS in autonomous commerce.

Problem¶

Traditional loyalty constructs (satisfaction–trust–commitment paradigm, NPS) assume a human executor and fail when AI agents become the primary decision-makers. They do not account for (1) algorithmic bounded rationality—technological architectures constraining the available option set—(2) constructed autonomy—perceived freedom bounded by algorithmic walls—or (3) the verifiable execution risks (gas costs, slippage, MEV, oracle manipulation, smart-contract exploits) that govern agentic brand preference in DeFi/tokenized settings.

Method¶

The DVM-HALL model decomposes brand utility into three layers and couples them with recursive update rules.

Human-side utility captures emotional equity, remembered satisfaction, perceived value, and normative/ethical fit: $$U^H_{hbt} = \theta_E E_{hbt} + \theta_S S_{hbt} + \theta_V V_{hbt} + \theta_N N_{hbt} + \epsilon^H_{hbt}$$

Agent-side utility captures machine-experience quality minus execution risk plus loyalty rewards: $$U^A_{hbt} = \beta^\top x^M_{bt} - \rho^\top r^{EX}_{bt} + \beta_R R^{loy}_{hbt} + \epsilon^A_{hbt}$$

where $x^M_{bt}$ includes API latency, reliability, and explainability, and $r^{EX}_{bt}$ includes DeFi-specific risks (Table 1).

Composite utility blends the two sides via a delegation coefficient $\delta_{ht} \in [0,1]$ and trust coefficient $T^a_{h,t} \in [0,1]$, with hard-constraint penalty $\Omega_{hbt}$: $$U_{hbt} = (1-\delta_{ht})U^H_{hbt} + \delta_{ht} T^a_{h,t} U^A_{hbt} - \Omega_{hbt}$$

Brand selection uses a softmax with temperature $\tau$: $$\Pr(Y_{ht}=b \mid h, a_h, B_t) = \frac{\exp(U_{hbt}/\tau)}{\sum_{k \in B_t}\exp(U_{hkt}/\tau)}$$

Dynamic updates: Trust and delegation are updated recursively after each execution using alignment $A_{ht}$, execution quality $Q_{ht}$, explanation quality $X_{ht}$, recourse quality $R_{ht}$, realized loss $L_{ht}$, and hard-constraint violations $VIO_{ht}$: $$T^a_{h,t+1} = \text{sigmoid}\!\left(\zeta_0 + \zeta_1 T^a_{h,t} + \zeta_2 A_{ht} + \zeta_3 Q_{ht} + \zeta_4 X_{ht} + \zeta_5 R_{ht} - \zeta_6 L_{ht} - \zeta_7 VIO_{ht}\right)$$

\[\delta_{h,t+1} = \text{sigmoid}\!\left(\kappa_0 + \kappa_1\delta_{ht} + \kappa_2 T^a_{h,t+1} + \kappa_3\frac{NHAS_{ht}}{100} - \kappa_4 Risk_{task,t} + \kappa_5 Control_{ht}\right)\]

NHAS scores each interaction $i$ on preference alignment $P_i$, economic efficiency $E_i$, execution reliability $R_i$, and explanation quality $X_i$, gated by hard-constraint satisfaction $H_i \in \{0,1\}$: $$S_i = 10 \cdot \text{clip}\!\left(H_i(0.35P_i + 0.25E_i + 0.20R_i + 0.20X_i),\ 0,\ 1\right)$$ $$W_i = \text{clip}\!\left(\mathbf{1}[S_i \geq 9] - \mathbf{1}[S_i \leq 6] - \lambda_F F_i - \lambda_{Priv}Priv_i - \lambda_{Comp}Comp_i,\ -1,\ 1\right)$$ $$NHAS = 100 \cdot \frac{1}{N}\sum_{i=1}^N W_i$$

Key Contributions¶

Formalization of brand selection under human-agent delegation as a dynamic, estimable softmax choice model with interpretable parameters for emotional equity, machine-experience quality, and execution risk.
First integration of DeFi execution risk variables (gas cost, slippage, MEV exposure, oracle risk, smart-contract risk, bridge risk, revocability) as first-class predictors of agentic brand preference.
Recursive trust and delegation update equations that allow post-execution recalibration.
NHAS metric: an auditable, risk-weighted alignment score sourced from human feedback, execution logs, benchmark comparisons, and verifiable receipts — proposed as a reward signal for agent fine-tuning and post-deployment monitoring.
Three-stage empirical validation roadmap: controlled human-agent shopping experiment, multi-agent market simulation, and DeFi/tokenized loyalty testbed.

Results¶

This is a purely theoretical paper. No experiments have been conducted. The validation plan is proposed but not yet executed. The only quantitative claim sourced from cited prior work is a 34% reduction in decision uncertainty tolerance associated with sustained AI recommendation reliance (attributed to Rehman 2026). No model coefficients, benchmark scores, or simulation outputs are reported.

Limitations¶

Entirely pre-empirical; all propositions remain unvalidated.
Transparent governance tooling required to mitigate trust miscalibration is stated as currently inadequate at operational scale.
Security and privacy barriers are expected to restrict adoption in emerging economies with low digital literacy and weak regulatory infrastructure.
No cross-cultural or cross-demographic validation of NHAS weights or loyalty parameters.
Empirical rate of trust decay when agentic execution conflicts with human emotional brand equity is uncharacterized.
Model coefficients ($\theta$, $\beta$, $\rho$, $\zeta$, $\kappa$, $\lambda$) are undefined and require estimation from proposed future studies.

Relevance to Agentic AI / LLM Agents¶

This paper directly addresses the governance and evaluation challenge that arises when LLM-based agents are granted purchasing authority: how to measure whether the agent's choices remain aligned with delegated human intent across repeated autonomous transactions. The recursive trust–delegation update model ($\delta_{h,t+1}$, $T^a_{h,t+1}$) provides a theoretical basis for studying how human oversight should scale dynamically with demonstrated agent reliability — a core open problem in agentic system design. The NHAS metric, if validated, offers a concrete scalar reward signal applicable to RLHF-style fine-tuning of commerce agents, extending beyond outcome correctness to include explainability and recourse quality. The DeFi execution layer also flags a class of deployment risks (MEV, oracle manipulation) not yet well-represented in mainstream LLM agent safety literature.