Can a module game a ledger by choosing when to sleep?

research/sleeping-incentives

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.

9 tests

What it found

Yes, if it declares after seeing its loss. The wealth ledger pays each awake module exactly its leave-one-out saving, ηW_A(1−p_i)S_i, but a module that sleeps whenever its own loss exceeds θ earns ηp_Bθ(1−θ)/2 per unit wealth against an equal-skill honest rival (best 1/8 at θ=1/2) and takes the market from a 0.1 share in about 130 rounds, while the router’s realised loss stays at 0.5. Declared before the router serves, the same wealth is a real saving that falls from 0.125 to 0.011 as the module’s signal about its own loss gets noisier. A sleeping tax that stops the exploit must be at least ηp_B/2, a fixed-share rate that halves an honest specialist asleep 90% of the time in 6 rounds, so commitment, not taxation, is the fix. Two modules, uniform losses, threshold strategies; mean-field predictions 3–8% slow.

A figure from its own output

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

Paper, code and results

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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.