NFT-Based Reward Mechanisms: Sybil Farming, Vesting, and Stochastic Verification

• The paper asks when NFT and ledger properties can help implement rewards, since NFT use alone does not solve participation rewards or issuer-controlled rules.Source: §1 · p. 1
• On high-throughput, low-fee ledgers, repeated automated claims are inexpensive, making verification and incentives increasingly important at scale.Source: §1 · p. 1
• Separate-account models give profitable farmers no finite scale; linking identities makes detection of one expose its cluster and gives attack size economic meaning.Source: §1 · pp. 1–2
• The analysis identifies a cluster-exposure penalty term and finds vesting alone is not optimal when marginal audit capacity cost at zero is zero; penalties and audits play distinct roles.Source: §1 · p. 2

2.1 What NFT rewards do and do not provide

• NFTs can record attendance, completion, access, contributions, or membership, and their records may be verified across applications when design and governance support it.Source: §2.1 · p. 2
• NFT programmes retain limitations: issuers control key rules, transferability can create resale and arbitrage opportunities, and technical requirements can add friction for genuine users.Source: §2.1 · p. 2
• The model treats an NFT as a record of a qualifying action and asks whether genuine activity can be rewarded without profitable false or duplicated claims.Source: §2.1 · p. 2

2.2 Platform characteristics

• Platform choice depends on transaction costs, throughput, finality, ecosystem maturity, governance, and user experience, with priorities varying by application.Source: §2.2 · p. 2, Table 1 · p. 3
• Hedera offers low predictable fees, high throughput, and fast finality, but its smaller NFT and DeFi ecosystem means rewards should not rely on secondary-market liquidity.Source: §2.2 · p. 2
• Low issuance costs also reduce the cost of fraudulent claims, motivating an incentive model that abstracts from any particular platform.Source: §2.2 · p. 3

3.1 Environment

• The issuer offers each qualifying identity a reward that vests after T periods; genuine and fraudulent claims have different costs and persistence probabilities.Source: §3.1 · p. 3
• Claims are audited independently each vesting period with probability a, and an audited fraudulent claim is detected with probability s; genuine claims pass in the baseline.Source: §3.1 · p. 3
• A claim that loses eligibility remains auditable during vesting, and a penalty applies even if it had already lost eligibility when detected.Source: §3.1 · p. 4

3.2 Cluster detection

• Linked identities can be reviewed as a cluster, with any detected identity causing whole-cluster forfeiture of rewards and a penalty F.Source: §3.2 · p. 4
• When cluster survival falls geometrically, the farmer's attack has a finite scale; without effective detection or vesting, a profitable attack has no finite scale.Source: §3.2 · p. 4
• The continuous relaxation gives a sufficient, conservative deterrence condition for the integer problem, where deterrence means no positive identity count is profitable.Source: §3.2 · p. 4

4 Deterrence

• When condition (3) fails, the continuous payoff has a unique positive maximizer and is strictly increasing before it and decreasing afterward.For the integer problem, the maximum lies at one of the two integers adjacent to that scale.Source: §4 · pp. 4–5
• Condition (3) is sufficient but not necessary for integer deterrence; when it fails, the farmer’s best integer scale is adjacent to the continuous maximizer.If that maximizer is below one, the relevant comparison is between zero and one identity.Source: §4 · pp. 4–5
• With perfect detection, farming is deterred for any penalty F ≥ 0, because every submitted claim is detected in the first audit period.The condition (3) test does not cover this case and it is handled separately.Source: §4 · p. 5

4.1 Reading the condition

• Condition (3) compares expected gross value per identity with its private cost and the added detection risk from exposing the whole cluster to a penalty.The cluster-detection term matters when the private cost of an identity is small.Source: §4.1 · p. 5
• Vesting lowers fraudulent claims’ payment probability while lengthening the audit window, but genuine participants bear only the payment-probability effect.This asymmetry is the source of vesting’s screening power; vesting also provides verification time, and the cluster-detection term vanishes if T, L(a), or F is zero.Source: §4.1 · pp. 5–6
• Without detection, deterrence reduces to q_F^T R ≤ k_F, and a profitable attack has no finite scale; cluster-level detection instead yields a finite optimum when s, a, and T are positive.If the reward is transferable at price p, replacing R with R + p makes deterrence harder and may require a higher horizon or audit rate.Source: §4.1 · p. 6

5.1 The deterrence frontier

• The minimum audit rate falls to zero by Tbar; deterrence is compatible with genuine participation iff Tmin≤Tmax, while vesting alone works iff Tbar≤Tmax.When the required audit rate exceeds one for short horizons, Tmin is the unique threshold where the rate reaches one.Source: §5.1 · pp. 6–7
• Vesting alone may undermine participation when genuine users are only slightly more persistent than farmers; horizon and penalty complement detection but can substitute for auditing along the frontier.A higher horizon or larger penalty allows a lower audit rate along the deterrence frontier.Source: §5.1 · p. 7

5.2 The designer’s problem

• Delay taxes genuine participants while verification costs the issuer; when marginal audit cost at zero is zero, the optimum uses positive auditing and vesting alone is never optimal.The result holds for both interior and boundary optima.Source: §5.2 · pp. 7–8
• With positive marginal audit cost at zero, sufficiently high linear audit costs can instead make vesting alone optimal; in the stated calibration, this occurs at d≥45.8.Whether auditing is worthwhile depends on audit-cost behavior near zero, not on a general property of the model.Source: §5.2 · p. 8

5.3 Boundary cases

• No policy with T=0 deters when R>kF; with no effective verification, only vesting deters and a profitable attack has unbounded scale.No audit periods exist at T=0, while a=0 or s=0 makes the payoff linear in identity count.Source: §5.3 · p. 8
• Penalties make detection consequential at any scale, while cluster-level auditing can deter without penalties in the integer problem even when the continuous optimum remains positive.In the calibration at T=4, the no-penalty condition binds at a=0.564, although the continuous optimum remains positive throughout the reported audit-rate range.Source: §5.3 · p. 9

5.4 Numerical illustration

• At d=40, the optimum is T*=4.15 and a*=0.30, with objective 26.6 versus 51.7 under vesting alone.The reported reduction is roughly one half.Source: §5.4 · p. 9

5.5 Extension: false positives

• With false-positive probability η<s, auditing also affects genuine participation; the extension modifies that constraint but leaves optimal (T, a) characterization for future work.The baseline optimal-policy results assume auditing has no cost for genuine participants.Source: §5.5 · p. 10

• Specify the qualifying action and verification evidence; costly or hard-to-automate activity raises kF, while easy automation may require stronger verification.Source: §6 · p. 10
• Persistent, verifiable NFT records are useful when rewards must be recognised across applications or organisations.Source: §6 · p. 10
• Transferability is a design choice: resale value can increase the return to farming, while non-transferable rewards suit credentials, reputation, attendance, and eligibility.Source: §6 · p. 10
• Auditing without a penalty can deter an integer attack by making the first identity unprofitable; a penalty adds a consequence when a cluster is detected.Source: §6 · pp. 10–11
• Cluster deterrence requires linked identities; device, funding, and behavioural signals may provide links, but linkage strength remains a separate design question.Source: §6 · p. 11
• Vesting can distinguish genuine users from farmers when persistence differs and provides time for audits; caps separately limit financial exposure.Source: §6 · p. 11
• Wallet, fee, and cryptocurrency requirements should stay low in broad-participation programmes because they enter kG.Source: §6 · p. 11

• Total forfeiture after one detection is a strong linkage benchmark; it fits traceable identities, not genuinely unlinkable ones, and partial-linkage effects remain conjectural.Source: §7 · p. 11
• The farmer is assumed risk-neutral and the penalty collectible; exclusion or reputational penalties may have uncertain, smaller effective value than their nominal value.Source: §7 · p. 12
• The reward R is exogenous, so the model does not solve the design trade-off between attracting genuine participation and increasing the return to farming.Source: §7 · p. 12
• A single farmer and uncapped pool omit attacker congestion and heterogeneity, which would produce strategic interactions or type-dependent attack scales.Source: §7 · p. 12
• Deployed-programme data could estimate model parameters and test the propositions, including whether c′(0) = 0 describes audit capacity.Source: §7 · p. 12

• NFTs’ main advantage in this analysis is a programmable, verifiable record of contribution, eligibility, access, or status; low-cost ledgers do not solve incentives.Source: §8 · p. 12
• Linked identities give the farmer a finite optimal scale and add the deterrence term TL(a)F; when audit capacity has zero marginal cost at zero, vesting alone is not optimal.Source: §8 · p. 12
• Token issuance is only one part of the mechanism; programmes also need verification, appropriate transfer rules, and incentives favouring genuine participation over strategic extraction.Source: §8 · p. 12