EIP-1559 Miner Incentives to increase Stategrowth

An under-discussed section of 1559 has been that burning the base-fee and awarding miners a flat tip to off-set their uncle-risk creates a direct incentive for miners to increase stategrowth through a new optimal mining strategy.

The Current Situation

Currently, miners have no incentives to adjust the gas limit because fee elasticity is approximately 1 (V. Buterin, "Estimating Cryptocurrency…"). This means that doubling the block size would mean that the transaction fee for users would halve, and the total reward for a block would remain approximately the same. Miner profit incentives are currently independent of state-growth concerns, which is an important situation since there are concerns about the fact that consumer SSDs haven't been growing as fast as the Ethereum state size. Ethereum node operators are currently unpaid, which means that we cannot expect them to continually improve their node by creating a RAID configuration or larger SSDs due to the cost.

Post-1559

The primary change that we are concerned about in 1559 is that burning the basefee and awarding miners a flat fee per gas unit creates a profit incentive for miners to increase the gas limit as well as increasing the likelihood of near-head reorgs caused by a high uncle-rate. The miner fee must be above the cost of inclusion, otherwise, it will be more profitable to submit a block without that transaction. If any transaction's miner fee is greater than the minimal cost of inclusion, then it will be profitable to add to a block since it raises the expected value of the block.

This creates an opportunity for miners to optimize their block's gas in order to obtain the most profit. Since the miner fee must be above the marginal cost of inclusion, shrinking or increasing the block may be the optimal way to increase profits. Incentives for running an Ethereum node aren't anticipated to increase before Eth 2.0 is released. This means that nodes won't be growing their capacity for state fast enough to keep up with miners, which will force them to centralize in the hands of people who manage to create profit incentives such as miners, exchanges, and individuals who want to hold their own Ethereum wallet.

Calculating the Most Profitable Block

marginal cost = .0115*gl^(2)/12,500,000
uncle rate = .046*gl/12,500,000
block profit = 2 - .25 uncle rate + gl * (average miner fee in block - marginal cost)
average miner fee in block = average miner fee per gas unit of the most valubale transactions that fit within the gas limit
Someone smarter than me can find the solution to this optimization problem, but worked out below, I show how increasing the gas limit increases the profit in a few example blocks.

Flat Fee Example

Consider a mempool containing 100,000,000 gas at a 5 gwei miner reward. We start by filling our theoretical block with 10,000,000 gas to represent the current model gives an expected value of 2.038. For 10,000,000 gas we estimate an uncle rate of 4%. We calculate the expected value for a 62,500,000 gas block and get 2.172 Eth on average. A 6.5% increase in profits in exchange for a 625% increase in the gas

Competing Fees Example Using Arbitrarily Chosen Miner Tips

Consider a mempool containing 100,000,000 gas with 10,000,000 gas at each gwei between 1 and 10. We start by filling the block with the 10 gwei transactions, giving us a block with an expected value of .04 * 1.75 + .96 * 2.1 = 2.086. Next, we add the 9 gwei gas which gives us an expected value of .08 * 1.75 + .92 * 2.19 = 2.1548. Still profitable, we repeat this calculation adding the next 10,000,000 gwei giving us the folowing results: 2.2076 for adding the 8 gwei transactions, 2.24 for adding the 7 gwei ones, 2.27 for the 6 gwei ones, 2.282 for the 5 gwei ones, the remaining 4 gwei transactions are below the minimal cost of inclusion of 4.8 gwei. Miners were able to increase profits by 9.3% by raising the gas limit by 480%.

Competing Fees Example Modeled Using Pareto's Law

Consider the current mempool currently holding 180,000,000 gas. If we follow pareto's law and assume that 144,000,000 of those transactions are willing to pay only 1 gwei. 28,800,000 are willing to pay 2 gwei. 5,760,000 are willing to pay 3 gwei, 1,152,000 are willing to pay 4 gwei, and the remaining 288,000 are willing to pay 5 gwei. When we add the 5 gwei transaction, the expected value becomes 2.001. Adding the 4 gwei transactions brings us to 2.005. Adding the 3 gwei transactions brings us to 2.016. Adding half of the 2 gwei transactions berings us to 2.028 Eth. At this point, we are now at 173% of the previous gas limit. If we add the rest of the 2 gwei transactions, we reach 2.037. This means that a 288% increase in the gas limit increased profits .7% by in comparison to the current gas limit at 12,500,000 gas with an expected value of 2.021