Multidimensional Blockchain Fees are (Essentially) Optimal

In this paper we show that, using only mild assumptions, previously proposed multidimensional blockchain fee markets are essentially optimal, even against worst-case adversaries. In particular, we show that the average welfare gap between the following two scenarios is at most $O(1/\sqrt{T})$, where $T$ is the length of the time horizon considered. In the first scenario, the designer knows all future actions by users and is allowed to fix the optimal prices of resources ahead of time, based on the designer's oracular knowledge of those actions. In the second, the prices are updated by a very simple algorithm that does not have this oracular knowledge, a special case of which is similar to EIP-1559, the base fee mechanism used by the Ethereum blockchain. Roughly speaking, this means that, on average, over a reasonable timescale, there is no difference in welfare between 'correctly' fixing the prices, with oracular knowledge of the future, when compared to the proposed algorithm. We show a matching lower bound of $\Omega(1/\sqrt{T})$ for any implementable algorithm and also separately consider the case where the adversary is known to be stochastic.