Phase II Proposal: Parameter Selection Under Uncertainty

Avalanche Staking Economics: Phase II Proposal

Project: Parameter Selection Under Uncertainty for Avalanche Staking

Team: Bonding Curve Research Group (BCRG)

Duration: 6 Months

Date: January 21, 2026

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Executive Summary

Following the successful completion of Phase I—which delivered foundational taxonomies, systems analysis, and a comprehensive differential specification—this proposal outlines Phase II: a focused investigation of the Avalanche staking subsystem using the Parameter Selection Under Uncertainty (PSUU) methodology.

Phase II will produce validated, actionable parameter recommendations specifically for staking subsystem, enabling the Avalanche Foundation to make data-driven decisions about validator rewards, staking duration, and yield structures.

Staking economics represents a top priority for the Foundation, with multiple community-initiated ACPs addressing validator and delegation mechanisms. This work delivers the analytical foundation for evidence-based governance decisions for staking, validating, and delegation mechanism parameterization for the Avalanche Network.

Key deliverables:

• Calibrated staking model validated against 2024-2025 historical data
• Sensitivity analysis revealing which governance levers most affect staking outcomes
• Parameter recommendation report with decision trees and correlation analysis
• Open source model and knowledge transfer workshops
• Analytic support for ACP development regarding staking incentives and parameterization

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Part I: Scope

Focus: The Staking Subsystem

Phase II narrows scope to the staking subsystem specifically, abstracting away other components of the full differential specification. This focused model will capture:

• Validator staking behavior
• Delegator staking behavior
• Reward mechanics and yield determination
• Duration-dependent incentive structures

Other subsystems (L1 ecosystem dynamics, fee markets) are treated as environmental inputs rather than endogenous components.

The Core Question

Under what “governance” configurations do Avalanche’s staking incentives sustain validator and delegator participation across bull markets, bear markets, and competing DeFi yields—while maintaining the security guarantees required by a multi-billion dollar network?

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Part II: Methodology

Parameter Selection Under Uncertainty (PSUU)

PSUU is a computational methodology developed by complex systems engineering firm Block Science for selecting robust parameters when system behavior is uncertain. Successfully applied to Subspace Network tokenomics, it systematically explores the relationship between governance decisions and system outcomes.

Fig 1: The PSUU pipeline—from environmental scenarios through simulation to ML-based parameter recommendations

How PSUU Works

Fig 2: The 4-step PSUU process flow

Step 1: Define the Design Space

• Identify controllable parameters (governance levers)
• Identify environmental scenarios (external uncertainty)
• Define KPIs and success thresholds

Step 2: Generate Simulations

• Cartesian product of all parameter combinations
• Multiple Monte Carlo runs per combination
• Result: thousands of simulation trajectories

Step 3: Aggregate and Analyze

• Compute KPIs for each trajectory
• Convert KPIs to binary utility outcomes (threshold met / not met)
• Apply machine learning to identify parameter-outcome relationships

Step 4: Produce Recommendations

• Decision trees showing parameter importance
• Correlation matrices linking levers to outcomes
• Parameter ranges optimized for single or multiple goals

Example Output: Decision Tree

Fig 3: Decision tree for goal optimization, with feature importance analysis

Example Output: Parameter Influence

Fig 4: Parameter influence on KPIs across simulation results

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Part III: The Design Space

The following represents an illustrative design space based on preliminary discussions. The actual design space, including specific parameters, ranges, scenarios, and KPIs, will be discovered collaboratively between BCRG and the Avalanche team and validated against real data during Milestone 1.

Controllable Parameters (Governance Surface)

These are policy levers the Avalanche Foundation can adjust. The current reward function is defined as:

$$Reward=(R_{max}-R_{current})\times \frac{S_{total}}{S_{supply}}\times \frac{t_{stake}}{t_{year}}\times C(t_{stake})$$

Where $C(t_{stake})$ is the consumption rate function governed by the parameters below, typically modeled as a linear interpolation between minimum and maximum yield bounds:

$$C(t_{stake})=Y_{min}+(Y_{max}-Y_{min})\times \left(\frac{t_{stake}-t_{min}}{t_{max}-t_{min}}\right)$$

Parameter	Description	Current	Exploration Range
MIN_STAKE_DURATION	Minimum lockup period	2 weeks	1 week – 3 months
MAX_STAKE_DURATION	Maximum lockup period	1 year	6 months – 2 years
MIN_DURATION_YIELD	APR for minimum duration	~6%	4% – 8%
MAX_DURATION_YIELD	APR for maximum duration	~8%	6% – 12%
CONSUMPTION_RATE_BOUNDS	Reward distribution parameters	Current	±20% variations
VALIDATOR_REWARD_SHARE	Split between validators/delegators	Current	60% – 90%

Environmental Scenarios (External Uncertainty)

Conditions beyond the protocol’s control that the system must be robust against:

Scenario	Description	Values
EXTERNAL_YIELD	Competing DeFi/TradFi yields	3%, 5%, 7%, 10%
MARKET_CONDITION	Crypto market sentiment	Bull, Neutral, Bear
NETWORK_GROWTH	L1 adoption rate	Low, Medium, High

Scenario Groups:

• Baseline: Expected conditions over simulation horizon
• Sustained Stress: Prolonged adverse conditions (bear market, high competing yields)
• Shock Events: Temporary disruptions (market crash, yield spike)

Behavioral Dynamics (Response Functions Calibrated from Data)

A key methodological advancement: behavioral parameters are modeled as state variables that evolve endogenously, not fixed constants.

Core Behavioral Parameters:

Parameter	Value (Spec)	Phase I Concept	Phase II Treatment
STAKING_SENSITIVITY	0.1	Fixed Stake Rate	State Variable: f(APR differential)
OPPORTUNITY_COST	5%	Fixed Unstake Rate	State Variable: f(External Yields)
AVG_RESTAKE_RATE	67%	Fixed Restake Rate	State Variable: f(Compounding Incentive)
COMMISSION_RATE	2-20%	N/A	Variable distribution parameter

Response Function Form:

Staking flows respond to the spread between APR and Opportunity Cost.

Note: The tanh function below is an illustrative reference implementation of bounded rationality. We are not biased toward this specific form; Phase II will empirically calibrate the optimal response function (e.g., logistic, piecewise linear) against historical data.

$$flow=SENSITIVITY\times supply\times max(0,tanh(APR-OPPORTUNITY\_COST))$$

Calibration approach:

1. Ingest Avalanche-provided historical data (2024-2025)
2. Fit the response functions (f) to observed stake/unstake patterns—these functions define how behavioral parameters evolve during simulation
3. Validate fitted functions against held-out data
4. Apply uncertainty bounds to function parameters for PSUU exploration

Key Performance Indicators

Aligned with the Differential Specification, we categorize success metrics into Security, Economics, and Stability:

Category	Indicator	Target Direction	Description
Security	STAKING_RATIO	50-60%	Optimal range for economic security vs. liquidity.
Security	VALIDATOR_COUNT	>1,000	Maintaining sufficient decentralization.
Security	DECENTRALIZATION	High (1-HHI)	Preventing stake concentration.
Economic	NET_INFLATION	Decreasing	Path toward deflationary crossover (burn > issuance).
Economic	VAL_PROFITABILITY	>0 (Sustainable)	Rewards + Fees must cover operational costs.
Stability	APR_VOLATILITY	Low Variance	Preventing erratic yield fluctuations.
Stability	STAKING_VOLATILITY	Low Variance	Preventing rapid mass unstaking events.

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Part IV: Model Validation

A critical methodological question: how do we evaluate whether the model matches reality?

Goodness-of-Fit Protocol

Approach:

1. Initialize model with actual state variables from January 2025
2. Run simulation forward through December 2025
3. Compare simulated trajectories to observed historical values
4. Compute goodness-of-fit metrics

Metrics:

Metric	Description	Target
Trajectory correlation	Pearson r between simulated and actual	> 0.90
RMSE (staking ratio)	Root mean squared error	< 2 percentage points
Direction accuracy	% of time trends match	> 85%
Turning point detection	Captures major inflections	Qualitative assessment

If validation fails: Iterate on behavioral parameter calibration until acceptable fit is achieved. This ensures the model’s sensitivity analysis reflects reality, not artifacts.

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Part V: Milestones & Deliverables

Milestone 1: Foundation (Months 1-2)

Focus: Data ingestion, model definition, behavioral calibration

Deliverables:

ID	Deliverable	Description
1.1	Data Ingestion	Ingest Avalanche-provided historical data (validator/delegator flows, rewards, durations)
1.2	Data Manifest	Documentation of sources, transformations, quality metrics
1.3	Staking Model Spec	Simplified model focused on staking subsystem with behavioral state variables
1.4	Behavioral Calibration	Fitted response functions for stake/unstake/restake with confidence intervals
1.5	Preliminary Validation	Initial goodness-of-fit assessment against 2024-2025 data

Success Criterion: Preliminary Validation Report delivered and approved by Avalanche team

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Milestone 2: Simulation & Analysis (Months 3-4)

Focus: PSUU implementation, Monte Carlo sweeps, sensitivity analysis

Deliverables:

ID	Deliverable	Description
2.1	PSUU Infrastructure	Full parameter sweep pipeline with cloud compute
2.2	Simulation Execution	50,000+ trajectories across governance × environment space
2.3	KPI Computation	Automated computation of all KPIs per trajectory
2.4	Validation Confirmation	Final goodness-of-fit achieving >90% correlation
2.5	Sensitivity Analysis	Decision trees and correlation matrices for all KPIs
2.6	Risk Surface Map	Parameter regions where staking incentives fail
2.7	Workshop #1	Model walkthrough and preliminary findings review

Success Criterion: Sensitivity Analysis Report delivered covering all key parameters

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Milestone 3: Delivery & Transfer (Months 5-6)

Focus: Recommendations, documentation, knowledge transfer

Deliverables:

ID	Deliverable	Description
3.1	Parameter Recommendation Report	Actionable guidance with decision framework
3.2	Scenario Playbook	”If X market condition, then Y parameter adjustment”
3.3	Open Source Release	Full model code with documentation
3.4	Workshop #2	How to run scenarios and interpret results

Success Criterion: Final Parameter Report delivered and Code Repository transferred

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Part VI: Timeline

Fig 5: 6-Month Project Timeline detailing parallel work streams and iteration cycles

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Part VII: Team

Role	Name	Responsibility
Project Lead	Hash Nabir	Stakeholder coordination, milestone management
Principal Researcher	Shawn Anderson	Model architecture, PSUU implementation, analysis
Data Engineer	Rex	Data analysis, simulation infrastructure
Domain Advisor	Jeff Emmett	Token economics, mechanism design, model review
Operations Support	Jessica Zartler	Coordination, documentation, publishing

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Part VIII: Success Criteria

Criterion	Measurement	Target
Model validity	Goodness-of-fit vs. historical data	>90% correlation
Analysis coverage	KPIs with significant sensitivity results	All defined KPIs
Recommendation clarity	Actionable parameter ranges delivered	Yes
Knowledge transfer	Avalanche team can run scenarios independently	Verified in workshop
Code quality	Open source, documented, reproducible	GitHub release

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Appendix A: Phase III Horizon

Beyond Phase II, opportunities exist for continued collaboration:

• ACP Advisory: Support community proposal development with simulation-backed analysis
• Ongoing Monitoring: Periodic model updates as network evolves
• Extended Scope: Apply PSUU to other subsystems (fee markets, L1 incentives)

These possibilities can be scoped after Phase II completion based on Foundation priorities.

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Appendix B: Reference Materials

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• Phase I Research
• Subspace PSUU Repository
• How to Perform Parameter Selection Under Uncertainty

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Proposal prepared by Bonding Curve Research Group

January 21, 2026