Farsighted miners under transaction fee mechanism EIP1559

We investigate the recent fee mechanism EIP1559 of the Ethereum network. Whereas previous studies have focused on myopic miners, we here focus on rational miners in the sense of having level-k foresight. We derive expressions for optimal miner behavior (in terms of setting block sizes) in the case of level-2 foresight for varying degrees of hashing power. Results indicate that a sufficiently large mining pool will have enough hashing power to gain by strategic foresight. We further use a simulation study to examine the impact of foresight for levels k > 2. In particular, the simulation study indicates that for realistic levels of hashing power greater than 10% miners/pools can not gain from the foresight of levels k > 2.