  In ZK-Rollups, provers spend significant computational resources to generate
validity proofs. Their costs should be compensated properly, so a sustainable
prover market can form over time. Existing transaction fee mechanisms (TFMs)
such as EIP-1559, however, do not work in this setting, as EIP-1559 only
generates negligible revenue because of burning, while provers often create or
purchase specialized hardware in hopes of creating long-term revenue from
proving, somewhat reminiscent of proof-of-work miners in the case of chains
like Bitcoin. In this paper, we explore the design of transaction fee
mechanisms for prover markets. The desiderata for such mechanisms include
efficiency (social welfare is maximized), incentive compatibility (it is
rational to bid honestly), collusion resistance (no profitable collusion among
provers exists), and off-chain agreement proofness (no profitable collusion
between users and provers exists). To demonstrate the difficulties of our new
setting, we put forward several simple strawman mechanisms, and show they
suffer from notable deficiencies.
