Economics of refereed verification

What it found

Inspection-game equilibrium for optimistic verification: stake substitutes for re-execution, extra verifiers dilute rewards (free-riding saturates), and joint tolerance/stake design under floating-point drift. Stylised model.

Paper, code and results

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

More in Verification games & slashing

• Bribing the verifiersBribing verifiers in refereed verification: closed-form bribe floor, a sharp collusion-proof stake that falls as 1/m, and jackpots that raise the floor one-for-one.
• Do verifiers and solvers learn the audit equilibrium?No-regret learning in the refereed-verification inspection game: conserved potential, closed-form cycle period, averages converge but per-round audit probability collapses; optimistic Hedge converges.
• Many verifiers, one solver: the volunteer's dilemma in refereed verificationM verifiers in the inspection game: detection pinned at s/(s+S), cheating rises with m under split rewards, symmetric equilibrium is a saddle (volunteer's dilemma), bandit learners need an exploration floor.
• Are stake and audits substitutes in trace verification?Sampled audits of committed training traces: payoff is convex in corrupted steps, deterrence iff min(F, f·k) ≥ T·g, so stake and audits are complements and stake must scale with job length.
• What does secret task assignment buy?Random k-fold replication with slashing against a colluding fraction β: secret assignment makes cheating a coordination game with unique-honesty stake Gβ^{k−1}/(1−β^{k−1}), public assignment leaves β^k corruption at any stake, and assignment leaks leave a λβ^k floor.
• How should a scarce audit budget be spread?Scarce audit budget across heterogeneous jobs: deterrence threshold g/(g+S) makes it a knapsack, greedy with a 1/3 guarantee (within 1% on 91% of instances), uniform audits need up to 1.9× the budget, heterogeneity lowers deterrence cost (Jensen), stake substitutes for audits.

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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.