Robust capacity parameter adjustment in Proo

Develop a robust capacity-parameter adjustment scheme for the Proo prover-market mechanism that adapts the batch capacity C to changing user demand and prover supply while remaining consistent with user and prover bids and avoiding both infeasibility (insufficient selected prover capacity) and inefficiency (excessively low capacity).

Background

Proo selects user transactions up to a fixed batch capacity C and then allocates proving to provers whose reported costs are at most the average per-constraint user fee, paying a uniform price. While analytically convenient, a fixed C can be mismatched to market conditions, causing either infeasibility (if C is set higher than the available prover capacity at the induced price) or inefficiency (if C is set too low, excluding high-value transactions).

The authors note that a practical prover market should adjust C in response to demand and supply, but this adjustment must conform to user and prover bids. They explicitly leave the task of devising a robust, principled adjustment rule as an open question.