Loyalty as Optimal Incentive Design in Crypto: Evidence from Uniswap v4 and a Relational-Contracts Lens

Abstract

In crypto incentive programs, “loyalty” is often dismissed as brand talk. We make a formal case that loyalty is optimal under incomplete contracts, drawing on Simon Board’s (2011) relational contracting framework. We pair the theory with public data from Gauntlet’s Uniswap v4 Month 2 campaign to quantify insider vs outsider effects, and we simulate policy rules that favor insiders unless an outsider’s advantage crosses a theoretically justified threshold. The resulting design playbook translates academic predictions into practical guidelines for mining programs, migrations, and hooks.

1. Theory: Loyalty as a response to holdup and rents

• Holdup: When transfers are not fully contractible, the agent can expropriate quasi-rents after specific investment. To avoid this, the principal must grant a rent to the agent.
• Endogenous fixed cost: Under a repeated relationship, the rent is paid once (via delayed utility), causing the first trade to behave like a fixed cost. This produces an insider–outsider divide: insiders are used efficiently; outsiders face a bias unless their advantage is large enough.
• Onboarding condition: The outsider must deliver surplus that exceeds the rent wedge, approximately (1 − δ)·v for discount factor δ and per-period value v.
• Comparative statics: As δ → 1, the optimal insider set expands and can be self-enforcing; with lower δ, loyalty is stricter.

This yields a clean rule: “Use insiders by default; onboard outsiders only when their expected surplus clears the (1 − δ)·v threshold.”

2. Data: Uniswap v4 Month 2 (Gauntlet)

Source: Gauntlet. Uniswap v4 Unichain Month 2 Liquidity Mining Retro (as-of 2025-06-12). We parsed all pool rows and computed insider/outsider metrics. Insiders are defined by pre-incentive TVL or Volume market share above a threshold (sensitivity below).

Key facts:

• Coverage: 19 pools.
• Persistence: corr(pre→current)
  • TVL MS: 0.593
  • Volume MS: 0.689
• Weighted ROI by incentives (all pools):
  • TVL ROI: $42.37 per $1
  • Volume ROI: $31.53 per $1
• Insider vs outsider (threshold 0.5% pre MS):
  • Insiders (n=6): TVL ROI $62.75; Volume ROI $11.67
  • Outsiders (n=13): TVL ROI $35.26; Volume ROI $38.46

Sensitivity to insider threshold (pre MS):

• 0.1% → insiders n=9: in_TVL_ROI $54.58; in_VOL_ROI $36.38 | outsiders: out_TVL_ROI $29.80; out_VOL_ROI $26.53
• 0.5% → insiders n=6: in_TVL_ROI $62.75; in_VOL_ROI $11.67 | outsiders: out_TVL_ROI $35.26; out_VOL_ROI $38.46
• 1.0% → insiders n=5: in_TVL_ROI $71.06; in_VOL_ROI $13.25 | outsiders: out_TVL_ROI $34.02; out_VOL_ROI $36.84

Interpretation:

• Insiders compound liquidity and stability (higher TVL ROI, high persistence).
• Outsiders are crucial for flow and market share expansion (higher Volume ROI at the 0.5% definition), but come with an onboarding “rent.”
• Findings align with Gauntlet’s narrative: correlated LST pairs are TVL-productive but volume-light; high-volume pairs and hook experiments drive trading and learning.

3. Policy simulation: Loyal vs myopic

We simulate two policies with i.i.d. U[0,1] costs across a large supplier set, period value v=1, rent charged once per new partner, and discount factor δ.

• Loyal: preferentially select insiders; admit outsider only if (value advantage) ≥ (1 − δ)·v.
• Myopic: always pick the period’s cheapest (no loyalty bias); pays the first-trade rent for many partners across time.

Present value (PV) profits over 5,000 periods, 50 agents:

• δ=0.90: PV_loyal 5.28 vs PV_myopic 0.99
• δ=0.95: PV_loyal 9.83 vs 4.13
• δ=0.98: PV_loyal 23.53 vs 22.56
• δ=0.995: PV_loyal 96.09 vs PV_myopic 155.39 (as δ→1, a broad insider set becomes efficient)

Implications:

• For realistic patience (δ≈0.90–0.98), loyalty dominates by amortizing rents and limiting churn.
• As δ approaches 1, the efficient insider set grows; do not stay too narrow—admit high-promise outsiders to increase average per-partner profit, consistent with Board’s comparative statics.

4. Design implications for incentive programs

• Backbone liquidity (insiders):
  • Maintain emissions for core pairs that underpin composability and credit markets (e.g., USDC/ETH, WBTC/USDT tiers, major LST/ETH where systemic).
  • Expect higher TVL ROI and persistence; monitor quality-of-liquidity signals (depth at touch, adverse selection) as relational health.
• Onboarding (outsiders):
  • Admit when expected volume surplus clears (1 − δ)·v; migrations (e.g., WBTC→WBTC0) and uncorrelated pairs can cleanly exceed the wedge.
  • Treat hook incentives as probation: require post-incentive retention and downstream protocol adoption to graduate into insiders.
• Budgeting and measurement:
  • Split ROI by insider/outsider; track corr(pre→current MS) as a “compounder score.”
  • Measure rent amortization: incentives per persistent $ of TVL and per persistent daily volume after tapering.
• Governance alignment:
  • Calibrate δ to organizational patience/runway; as δ rises, responsibly expand insiders. As δ falls, tighten onboarding thresholds.

5. Why this is actionable for Gauntlet and rigorous for academia

• Gauntlet: Provides a principled rule to segment spend, schedule migrations, and scale hook experiments. It predicts when to push volume vs when to harden liquidity, with empirically checkable KPIs.
• Academic rigor: Onchain settings uniquely enable tests of relational-contract predictions (endogenous switching costs, insider bias, employment-like contracts via continual rewards)—inviting collaborations to estimate δ-like patience and pool-specific rent wedges.

Methods

• Parsing and metrics computed from the Month 2 retro table;
• Insider thresholds evaluated at 0.1%, 0.5%, and 1.0% pre-incentive MS.
• Simulation approximates Board’s insider–outsider logic with a one-time rent and the (1 − δ)·v admission rule.

Conclusion

Loyalty, precisely defined, is optimal contract design under onchain frictions. Programs that amortize onboarding rents and grow a high-quality insider set will convert emissions into durable market power. The theory predicts—and the Uniswap v4 data supports—that disciplined loyalty paired with targeted outsider onboarding outperforms opportunistic switching.

References Board, S. (2011). Relational Contracts and the Value of Loyalty. American Economic Review, 101(7): 3349–3367

Gauntlet. Uniswap v4 Unichain Month 2 Liquidity Mining Retro (as-of 2025-06-12)