Abstract: In blockchains such as Bitcoin and Ethereum, users compete in a transaction fee auction to get their transactions confirmed in the next block. A line of recent works set forth the desiderata for a "dream" transaction fee mechanism (TFM), and explored whether such a mechanism existed. A dream TFM should satisfy 1) user incentive compatibility (UIC), i.e., truthful bidding should be a user's dominant strategy; 2) miner incentive compatibility (MIC), i.e., the miner's dominant strategy is to faithfully implement the prescribed mechanism; and 3) miner-user side contract proofness (SCP), i.e., no coalition of the miner and one or more user(s) can increase their joint utility by deviating from the honest behavior. The weakest form of SCP is called 1-SCP, where we only aim to provide resilience against the collusion of the miner and a single user. Sadly, despite the various attempts, to the best of knowledge, no existing mechanism can satisfy all three properties in all situations.

Since the TFM departs from classical mechanism design in modeling and assumptions, to date, our understanding of the design space is relatively little. In this paper, we further unravel the mathematical structure of transaction fee mechanism design by proving the following results:

- Can we have a dream TFM?

- Rethinking the incentive compatibility notions.

- Do the new design elements make a difference?