What does not knowing the horizon cost a market maker?

What it found

An LMSR with liquidity b routes like Hedge with rate 1/b, but the tuned b needs the horizon T. A b_t = c√t schedule with c* = 1/(2√ln N) pays exactly √2 over the horizon-aware bound (1.36 rising to 1.41 measured); the doubling trick is 1.70× worse than the continuous schedule against a price-reactive adversary; and self-tuning liquidity b_t = Δ_t−1/ln N makes the subsidy equal the accumulated mixability gap (1.3 against 102 on easy data) with regret at most 2Δ. Regret analysis only. Stylised.

A figure from its own output

Paper, code and results

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

More in Prediction-market design

• The subsidy cost of privacy in prediction marketsDifferentially private LMSR via the binary-tree mechanism: path-wise loss bound, and the accuracy/subsidy cost of privacy.
• Who pays for the information in a manipulated market?Manipulating an LMSR verification market: manipulator loss b·KL(q‖τ) equals the extra informed rent, and manipulation raises accuracy only in a liquidity band (thin: costs 1−2q; deep: neutral).
• What does a slippage limit give away in a prediction market?Sandwiching an LMSR verification market: attacker profit is exactly the victim's slippage tolerance times its fair cost, needs capital ≈ εb/(1−p), dies to a fee ≈ v(1−p)/(2b); pro-rata batching keeps 99% of the extraction, random ordering cuts it 3×.
• Who trades decides how liquid a verification market should beGlosten–Milgrom vs LMSR for a verification market: informed share fixes b* = 1/(2 atanh m) (verified to 2e-16), peak misspecification regret is scale-free and overconfident b costs 1.5–2.4× more, LMSR subsidy → b* ln 2 is the spread GM charges.
• What does a fee do to a prediction market’s price?Proportional fees on an LMSR verification market: exact no-trade band [q/(1+f),(q+f)/(1+f)], price lag q/(1+f), dead-market cliff f ≥ 2a−1 (threshold 2 atanh f at ½), exact fee revenue f·b·ln((1−p₀)/(1−p_T)), and a break-even fee that costs +38% Brier error.
• What is a seat in a prediction market worth?Sequential LMSR seat rents are conditional mutual information: they telescope to the maker's expected loss (≤ b ln 2), fall with position at the Chernoff rate, order only redistributes a fixed total, and entry costs make error fall only ~1/b in the subsidy.

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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.