How should a router treat modules that are usually asleep?

research/sleeping-ledger

A self-financed wealth ledger for specialist modules that sleep: total wealth conserved exactly, sleeping wealth frozen (one private ledger per regime), regret ≤ ln(1/π_i)/η + η·n_i in the module's *own* awake time, entry of a module with wealth ε costs incumbents ln(1/(1−ε))/η; matches the regime oracle (0.1004 vs 0.1000) where forced-to-report Hedge sits at 0.30 and fixed share is worse.

8 tests

What it found

If only awake modules report and each awake module’s wealth is multiplied by 1+η(ℓ̂−ℓ_i), the ledger is exactly budget balanced, sleeping wealth never moves (each regime keeps a private ledger), and a module’s regret against the market on its awake rounds is at most ln(1/π_i)/η + ηn_i in its own awake time (the exponential variant pays ηT/8 and is not budget balanced). Admitting a module with wealth ε costs each incumbent ln(1/(1−ε))/η in its bound. With recurring regimes the ledger matches the per-round oracle (0.1004 vs 0.1000, regret about 2.7 whatever the number of specialists) while a forced-to-report Hedge sits at the generalist (0.30) and fixed share is worse (0.34–0.36). The bound is loose (measured regret 2.7 against a bound near 10³); losses bounded, wake sets exogenous.

A figure from its own output

Figure produced by research/sleeping-ledger: entrant_regret — sleeping-ledger/experiments/entrant_regret.svg, written by the project's own experiment code.

Paper, code and results

More in Markets as routers

Can a module game a ledger by choosing when to sleep?When may a module choose to sleep? The ledger pays exactly leave-one-out savings ηW_A(1−p_i)S_i; sleeping *after* seeing losses gains wealth ηp_Bθ(1−θ)/2 (best 1/8) and takes the market in ~130 rounds with the router's loss unchanged; committed *before* serving it is a real saving; the deterring tax ηp_B/2 is a fixed share that halves honest specialists in 6 rounds.
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How much liquidity does a payment system need, and what do netting and gridlock resolution save?Does bilateral or multilateral netting, or gridlock resolution, save a payment system liquidity? A simulator fitted to Bech and Soramäki's Danish and Finnish bounds (34.7% and 10.1% of gross value against the published 37.2% and 10.7% for DK) shows reciprocal flows are what make netting work, and resolution cuts delay by 24–46% in the Danish-shaped system but 34–62% in the Finnish-shaped one, where the paper found about 10%.
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All 13 Markets as routers projects →

Other research topics

Proper scoring & elicitation28 Effort & peer prediction9 Verification games & slashing19 Detection & tolerances14 Markets as routers13 Prediction-market design9 Paying contributors8 Decentralised training systems23 Digital twins & sim-to-real164 LLM chip design loops40 Robot manufacturing loops53 Ambient AI assistant46 Self-replicating manufacturing34 Simulation-first design64 Engineered clothing45 Task-specific AI accelerators40 Algorithmic chip-design loops42 Open-source purpose-built robots44 The software-engineering loop43 Adversarial human imitation41 Open-source residential construction41 Autonomous multi-angle capture34 Sensing, imaging and 3D31 Energy supply and dense energy storage39 Robot societies among people31 Agentic co-design of low-cost robots27 Laundry-hanging robots25 Machine learning on qualitative data23 Robots on the building site27 Civilizations & group psychology1 History & 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.