Escalating bonds: cheap challenges, fixed deterrence, a γ-fold capital asymmetry

What it found

Bond-escalation dispute games with a fallible oracle, solved exactly: the opening bond that deters false challenges is εV/((1−ε)C−εD) and shrinks geometrically in rounds (20.4 to 10⁻⁵) while the attacker's total outlay barely moves (20.41 to 20.62); against a capital-limited attacker the honest defender needs exactly γ·max{C(r)≤B_C} ≤ γB_C, so the responder pays γ per exchange. 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 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.
• When do verifiers complement rather than substitute?Verifiers as informational complements: decision value is zero below a closed-form committee size while mutual information is submodular; myopic hiring buys nothing and leave-one-out pay is a sawtooth that vanishes.
• How big should a random verifier committee be?Verifier committees from a finite pool: exact hypergeometric capture (zero once m ≥ 2B+1, up to 26× below binomial), exact size ≈0.90 of ln(1/ε)/KL(½‖β) vs Hoeffding up to 2.2× too large, stake-weighted draws depend only on Byzantine stake share (20 of 100 nodes at 4× stake capture a 41-committee w.p. ½), and the threshold safety/liveness trade-off.

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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.