Can cryptography and Bayesian equilibrium circumvent the TFM impossibility results?

Determine whether cryptographic enforcement of transaction fee mechanisms—such as in the multi-party computation (MPC)-assisted model—together with Bayesian notions of equilibrium can yield finite-block transaction fee mechanisms that overcome the paper’s impossibility results by simultaneously achieving appropriate incentive-compatibility and collusion-resilience properties (e.g., user incentive compatibility, miner incentive compatibility, and OCA-proofness or global side-contract-proofness).

Background

The paper proves strong impossibility results for transaction fee mechanisms (TFMs) under finite block size: no (possibly randomized) direct-revelation TFM can simultaneously satisfy user incentive compatibility (UIC), miner incentive compatibility (MIC), and OCA-proofness; and no (possibly randomized) TFM can satisfy UIC, MIC, and global side-contract-proofness (global SCP).

The authors discuss whether augmenting the model with cryptographic enforcement (e.g., MPC-assisted TFMs) and relaxing to Bayesian notions of equilibrium might circumvent these impossibilities. Prior work shows some feasibility (e.g., UIC, MIC, and 1-SCP in an MPC-assisted setting) but also impossibility for larger coalitions, motivating a precise question about whether cryptography and Bayesian equilibrium notions can overcome the new impossibility results established in this paper.