Confirmation of Bitcoin transactions is executed in blocks, which are then stored in the Blockchain. As compared to the number of transactions in the mempool, the set of transactions which are verified but not yet confirmed, available space for inclusion in a block is typically limited. For this reason, successful miners can only process a subset of such transactions, and users compete with each other to enter the next block by offering confirmation fees. Assuming that successful miners pursue revenue maximization, they will include in the block those mempool transactions that maximize earnings from related fees. In the paper we model transaction fees as a Nash Equilibrium outcome of an auction game with complete information. In the game the successful miner acts as an auctioneer selling block space, and users bid for shares of such space to confirm their transactions. Moreover, based on expected fees we also discuss what the optimal, revenue maximizing, block size limit should be for the successful miner. Consistently with the intuition, the optimal block size limit resolves the trade-off between including additional transactions (which possibly lower the unit fees collected) and keeping the block capacity limited (with, however, higher unit fees).
69outstanding transactions, and this is why users compete with each other for space, by proposing fees to confirm their exchanges in the next block. [4][5][6][7][8][9][10] This paper discusses the latter kind of competition, interpreting transaction fees as price bids submitted by the users to obtain (buy) a share of the available block space for transaction confirmation. Under such an interpretation, competition for block space can be seen as an auction, with the successful miner acting as an auctioneer, selling space for confirmation, and the proposed transaction fees acting as price bids to obtain shares of the available space. 11 We are not aware of such an approach to investigate the block size limit and transaction fees, with the closest in the existing literature being perhaps the work by Lavi (et al.) ("Redesigning Bitcoin's Fee Market," 2017). 9 Given the block capacity, the transaction size and associated proposed fees will determine which exchanges are confirmed in the next block. For this reason, users compete to enclose their transactions among those maximizing the miner's revenue. In so doing they face a fundamental trade-off: the higher the fee offered, the more likely it is for a transaction to be confirmed soon, but the more expensive-in case of confirmation-the payment will be. For this reason, the proposed fee is likely to be the outcome of a strategic decision. Namely, how large a fee to offer may depend also on what the other users are expected, or known, to offer.The problem bears similarities with the well-known Rucksack Problem, 12 though with a main difference. More specifically, in our approach a variation in the block capacity would typically affect the proposed transaction fees, while in the classical Rucksack problem this does not take pl...