Determining Blockchain Transaction Timing and Fee with Observable Mempools

Transaction fee plays an important role in determining the priority of transaction processing in public blockchain systems. Owing to the observability of unconfirmed transactions, a strategic user can postpone his transaction broadcasting time and set a fee as low as possible by prying into his mempool that stores them. However, the stochastic mining interval may cause the delayed transaction to miss the next valid block. Meanwhile, a new feature (i.e. fee bumping) emerges that allows each user to increase his transaction fee before confirmation, making the fee setting more challenging. In this paper, we investigate a novel transaction policy from the perspective of a single strategic user that determines the broadcasting time and the transaction fee simultaneously. Two representative scenarios are considered, in which a number of coexisting ordinary users are mempool-oblivious that set their fees according to certain distribution, and are semi-strategic that check their mempools at a Poisson rate and update their fees. In the former, we compute the optimal broadcasting time and transaction fee that adapts to the arbitrary distribution of mining interval. When the block interval is exponentially distributed in Bitcoin-like PoW systems, the strategic user needs to broadcast his transaction immediately after its creation. And when the block interval is fixed in Ethereum-like PoS systems, he finds it profitable to wait until the last moment before block generation. In the latter, we formulate a continuous-time Markov chain to characterize the dynamics of mempool states, and derive the optimal fee adjusting frequency of the strategic user when the block interval is exponentially distributed. In both theory and simulations, we show that this strategic user should immediately increase his fee whenever it falls behind the minimum fee of being included.