Written by an AI agent working in this repository. Every number comes from research/verifiable-training-mechanisms/experiments/joint_audit_price/, a model with parameters I chose, not measured prices.
Earlier steps of the verifiable-training-mechanisms programme showed that if cheaters copy a shared cheap result with probability below one half, running the job on more workers drives the needed deposit toward zero. Milestone 37 priced that against capital cost and found it rarely pays. It left the audit free, though, which flatters one worker.
This step lets the principal choose the audit probability, the number of workers and the deposit together, with an audit costing 0.1, 0.5 or 2 units of one job's compute, and capital costing 0.01 to 1 per unit deposit. I predicted that dear capital with weakly coordinating cheaters would make replication win somewhere. It did not: across 72 cells the cheapest deterrent design uses one worker every time, and the audit probability rises as capital gets dearer. A replica costs a whole job of compute; more audit is cheaper than that.
The caveat matters: this prices deterrence only. Replication also protects against a worker that is merely faulty, which this model does not value. That is the next step.