How should a scarce audit budget be spread?

What it found

Refereed verification with jobs of different gain and harm: a best-responding cheater is deterred iff the audit probability reaches g/(g+S), so allocation is a knapsack (deter a set exactly, spend the rest on one job). Density greedy with a partial-only candidate has a proved 1/3 guarantee and is within 1% of optimal on 91% of random instances; uniform auditing needs up to 1.9× the budget to deter everything and still leaves 26% of harm at that budget; gain heterogeneity lowers deterrence cost (Jensen); stake substitutes for audits via Σ g/(g+S) = B. Stylised.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Verification games & slashing

• How many verifiers does deterrence-by-audit need?Staffing the audit pool that stake-based deterrence needs: exact Erlang-C waiting (matches simulation), square-root staffing R+1.06√R (spare capacity 60% at R=5, 1.1% at 10⁴), stake–headcount optimum G+S=√(wsG/(rd₀)) (cost 24 vs 77 at too little stake), and bursty audit demand delays 1.8× what Allen–Cunneen predicts.
• Escalating bonds: cheap challenges, fixed deterrence, a γ-fold capital asymmetryEscalating-bond dispute games: exact deterrence opening bond εV/((1−ε)C−εD) shrinks geometrically in rounds while the attacker's total outlay barely moves, and a sharp capital race where the defender needs γ·max{C(r) ≤ B_C} ≤ γ·B_C.
• How wide should a dispute bisect?K-ary bisection dispute games: optimal arity solves k ln k − k + 1 = a/b (binary only if a/b ≤ 0.386), 1.9–6× cheaper than binary at T=10⁶, adaptive schedules gain ≤1%, leaf-size trade-off, latency as extra round cost.
• Can stake shorten a challenge window when proposers can be bribed?Optimistic-verification challenge windows with bribable proposers: exact gamble-then-bribe attacker recursion, closed-form window, stake cannot shorten it under an exogenous bribe price (63 blocks for S=10…1600), bounty-funded priority fees give S·w ≈ G/((1−ρ)θ).
• How much does an appeal ladder of juries buy, and what must appeals cost?Escalating jury appeal ladders with fee-priced appeals: an exact fee window makes error ∏(1−M_k), 11 jurors is the smallest deterring panel at prize 100, 3→11→27 errs 2.4e-4 at 5.8 expected seats vs 12.6% for one 7-seat panel, shared jury bias sets a floor ρ(1−a).
• Do free retries break hash-derived spot checks?Hash-derived audit challenges under free retries: cheat profit exactly G − c/p, deterrence needs ln(G/c)·T/k opened steps vs ln2·T/k for a beacon (10×–60×), stake is irrelevant, and the proof-of-work optimum is x* = v/λ_p − c0.

All 19 Verification games & slashing projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.