Behavioral Scoring for Uniswap

• The Behavioral Scoring Framework for Uniswap is an analytical system that uses on-chain liquidity and swap data to evaluate risk, performance, and strategic behavior.
• It employs a hybrid approach combining rule-based models, agent-based simulation, and neural network scoring to measure trading efficiency and market impact.
• The framework guides protocol design by informing adaptive fee schemes, risk management, and incentive alignment within decentralized exchanges.

A behavioral scoring framework for Uniswap is an analytical and algorithmic system that uses quantitative and contextual signals observable from on-chain user activity—primarily liquidity provision and swap behavior—to assess the strategic quality, stability, and risk profile of participants. This concept leverages economic models, agent-based simulation, neural scoring, and empirical data analysis to synthesize robust, role-specific reputation metrics, thereby supporting improved risk management, incentive alignment, and protocol governance within decentralized exchange environments.

1. Mathematical and Economic Foundations

Uniswap’s behavioral scoring frameworks are rooted in rigorous formalism. The Constant Product Market Maker (CPMM) defines trading via the invariant

$$(R_\alpha - \Delta_\alpha) \cdot (R_\beta + \gamma \Delta_\beta) = k$$

where $R_\alpha, R_\beta$ are asset reserves, $\gamma$ is the fee factor, and $k$ is the product constant (Angeris et al., 2019). Agents’ efficiency is assessed relative to optimal arbitrage expressions (subject to CPMM constraints) and no–arbitrage bands: $\gamma m_p \leq m_u \leq \gamma^{-1} m_p$ where $m_p$ is a reference market price and $m_u$ the Uniswap marginal price.

Additionally, risk-adjusted trade efficiency may include convex cost penalties, such as: $$f_{\alpha}(\Delta) = \frac{\rho_\alpha}{2} \Delta^2$$ or second-derivative-based slippage assessment,

$$\left.\frac{d^2}{d\Delta^2}\right|_{\Delta=0} = \frac{2 m_u}{\gamma R_\beta}$$

describing price impact mitigation with increasing reserves. These and their generalizations, e.g., constant mean markets, inform scoring metrics that benchmark observed behaviors (arbitrage, liquidity adjustments) against dynamic, economically optimal strategies.

2. Agent-Based Simulation and Empirical Behavioral Quantification

Large-scale simulations instantiate agents—arbitrageurs, liquidity providers (LPs), and swappers—with explicit incentive models (Angeris et al., 2019). Arbitrageur performance is quantified by deviation from theoretical price-bounding and efficiency in returning pool prices to equilibrium. LPs are scored for portfolio optimization, rebalancing frequency, and alignment with aggregate pool conditions.

Empirical studies on real Uniswap data show that most LPs are conservative, with 70%+ investing in a single pool and rarely reacting to short-term volatility (Heimbach et al., 2021). Return decomposition by pool type (stable, normal, exotic) is critical: e.g., daily returns in stable pools are dominated by predictable fee income, while those in exotic pools are high-variance, frequently negative due to impermanent loss. Return, fee income, and impermanent loss are formalized by: $$\text{Fees}_{t_1 \rightarrow t_2} = 100 \cdot \left(1 - \frac{\sqrt{k_{t_1}}}{\sqrt{k_{t_2}}}\right)$$

$$\text{ImpermanentLoss}_{t_1 \rightarrow t_2} = 100 \cdot \left(\frac{2 \sqrt{p_{t_2}/p_{t_1}}}{1 + (p_{t_2}/p_{t_1})} - 1\right)$$

Behavioral scores incorporate such risk and return calculations, sensitivity to market and external incentives (such as liquidity mining), and liquidity concentration/diversification patterns.

3. Machine Learning-Based Scoring and Role-Specific Modeling

Recent frameworks adopt a hybrid architecture for fine-grained role-specific scoring (Kandaswamy et al., 28 Jul 2025). For Uniswap, two scores are defined: a Liquidity Provision Score and a Swap Behavior Score.

The scoring pipeline comprises:

• Rule-based blueprints which compute soft scores from on-chain features such as deposit/withdrawal volume, frequency, holding periods, and withdrawal discipline for LPs, as well as swap volume/frequency and token diversity for swappers.
• Deep residual neural networks (DeepMLP_ResNet) refine these blueprints using densely connected skip connections inspired by U-Net, learning feature interactions and handling ambiguous cases via noise-augmented targets:

$$x_{\text{out}} = \text{LayerNorm}\left(x_{\text{in}} + \text{Dropout}(\text{Linear}(\text{SiLU}(\text{Linear}(x_{\text{in}}))))\right)$$

• Contextualization: Pool-level features (Total Value Locked, fee tier, pool size) are appended, ensuring behavioral assessment is robust to pool risk heterogeneity.

Experimental results on Uniswap v3 data show that 91.79% (LPs) and 90.83% (swappers) of predictions fall within a ±50 tolerance window of the blueprint ground truth, indicating robust ordinal preservation and interpretability in scoring.

4. Advanced Risk Modeling and Strategic Behavior

Uniswap v3’s concentrated liquidity and dynamic LP strategies introduce nuanced behavioral assessment possibilities. Strategic provision is formalized via mean–variance utility optimization over price intervals (Fan et al., 2021, Bayraktar et al., 13 Apr 2024): $$V(j_1, j_2;\theta,\ell^0) = \mathbb{E}_{\xi,\delta}[\pi(j_1, j_2, \xi;\theta,\ell^0)] - \lambda\, \text{Var}_{\xi,\delta}(\pi(j_1, j_2, \xi;\theta,\ell^0))$$ where the decision variables are tick interval endpoints ($j_1, j_2$), agent type ($\theta$), and aggregate pool liquidity profile ($\ell^0$).

Game-theoretic perspectives extend to Stackelberg games involving Maximal Extractable Value (MEV) bots and JIT liquidity attacks (Bayraktar et al., 13 Apr 2024). Equilibria are computed where LPs anticipate strategic bot insertion/removal, and scoring can reward agents whose allocations maximize collective resilience or predictive accordance with mean-field equilibria. Predictive calibration against real pool distributions yields tight Wasserstein-1 errors, validating model fidelity.

5. Pool and Ecosystem Health Metrics

Ecosystem-level assessment introduces "health" metrics based on macroscopic AMM analogies, e.g., the "ideal crypto law" (Miori et al., 2022): $$P_{\text{vol}} \cdot V_{\text{stab}} = n_{\text{fee}} \cdot R_{\text{pool}} \cdot T_{\text{liq}}$$ where $P_{\text{vol}}$ is daily trade volume, $V_{\text{stab}}$ is inverse price volatility, $T_{\text{liq}}$ is pool liquidity, and $n_{\text{fee}}$ the reciprocal of the fee tier. The cryptoness score ($\xi$)—the fit quality to the law—systematically ranks pool health and is proposed as a behavioral and regulatory monitoring tool.

Machine learning applications also compute decentralization indices (Shannon Entropy, HHI, Gini, Nakamoto Coefficient) from daily transaction data, contextualizing individual behavior within broader network equity and risk landscapes (Chemaya et al., 2023). These metrics are key for comprehensive risk models and dynamic scoring.

6. Protocol Extensions, Reputation Systems, and Incentive Mechanisms

Behavioral scoring frameworks extend naturally into protocol-level reputation and incentive systems. The "zScore" framework (not to be confused with the Uniswap-specific contextual zScore) aggregates wallet-level behavioral features, with neural weights and cluster-interval scaling: $z(f, l) = L[l] \times \sum_{n=1}^k a_n f_n$ where $f$ encapsulates on-chain behavioral features, $a_n$ are learned weights, and $L[l]$ is the lower interval bound for the assigned behavioral cluster (Udupi et al., 17 Feb 2025). The system can incorporate zero-knowledge proofs of real-world credentials (zkTLS), and is readily applicable to Uniswap for dynamic fee adjustments, MEV protection, and eligibility for privileged protocol features.

Consensus-oriented scoring models, including Proof-of-Behavior, formalize decentralized reputation at the consensus level through layered utility scoring: $$U_{\text{total}}(B) = U_{\text{motivation}}(B) + U_{\text{behavior}}(B)$$ Weights adapt dynamically: $$W_i(t+1) = (1-\rho) W_i(t) + \rho\, \frac{U_i(t)}{\sum_k U_k(t)}$$ offering prompt demotion of malicious actors and proportional incentive alignment (Borjigin et al., 27 Jun 2025). Fraud acceptance rates and proposer fairness are dramatically improved versus PoS baselines, as evidenced in simulation.

7. Practical Implications and Future Directions

Behavioral scoring in Uniswap enables protocol-aligned segmentation of agent behaviors, granular risk assessment, and design of nuanced incentive structures. Protocols can preferentially reward users based on long-term commitment, stable liquidity provision, disciplined trading, and proactive risk management. Simulation and empirical calibration (via Wasserstein distance, MAPE, or contextual accuracy) ensure models reflect real-world pool and participant evolution.

Applications extend from adaptive fee schedules and reward distributions to ecosystem health monitoring, regulatory reporting, and dynamic consensus governance, laying a foundation for resilient, efficient, and trustworthy decentralized exchange systems.