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In recent years, prominent blockchain systems such as Bitcoin and Ethereumhave experienced explosive growth in transaction volume, leading to frequentsurges in demand for limited block space and causing transaction fees tofluctuate by orders of magnitude. Existing systems sell space using first-priceauctions; however, users find it difficult to estimate how much they need tobid in order to get their transactions accepted onto the chain. If they bid toolow, their transactions can have long confirmation times. If they bid too high,they pay larger fees than necessary.  In light of these issues, new transaction fee mechanisms have been proposed,most notably EIP-1559, aiming to provide better usability. EIP-1559 is ahistory-dependent mechanism that relies on block utilization to adjust a basefee. We propose an alternative design -- a {\em dynamic posted-price mechanism}-- which uses not only block utilization but also observable bids from pastblocks to compute a posted price for subsequent blocks. We show its potentialto reduce price volatility by providing examples for which the prices ofEIP-1559 are unstable while the prices of the proposed mechanism are stable.More generally, whenever the demand for the blockchain stabilizes, we ask ifour mechanism is able to converge to a stable state. Our main result providessufficient conditions in a probabilistic setting for which the proposedmechanism is approximately welfare optimal and the prices are stable. Our maintechnical contribution towards establishing stability is an iterative algorithmthat, given oracle access to a Lipschitz continuous and strictly concavefunction $f$, converges to a fixed point of $f$.

Dynamic Posted-Price Mechanisms for the Blockchain Transaction Fee Market