Game-Theoretic Attacks

There is also another argument to bolster the case for inflation. This is that relying on transaction fees too much opens up the playing field for a very large and difficult-to-analyze category of game-theoretic attacks. The fundamental cause is simple: if you act in a way that prevents another block from getting into the chain, then you can steal that block’s transactions. Hence there is an incentive for a validator to not just help themselves, but also to hurt others. This is even more direct than selfish-mining attacks, as in the case of selfish mining you hurt a specific validator to the benefit of all other validators, whereas here there are often opportunities for the attacker to benefit exclusively.

In proof of work, one simple attack would be that if you see a block with a high fee, you attempt to mine a sister block containing the same transactions, and then offer a bounty of 1 BTC to the next miner to mine on top of your block, so that subsequent validators have the incentive to include your block and not the original. Of course, the original miner can then follow up by increasing the bounty further, starting a bidding war, and the miner could also pre-empt such attacks by voluntarily giving up most of the fee to the creator of the next block; the end result is hard to predict and it’s not at all clear that it is anywhere close to efficient for the network. In proof of stake, similar attacks are possible.

How to distribute fees?

Even given a particular distribution of revenues from inflation and revenues from transaction fees, there is an additional choice of how the transaction fees are collected. Though most protocols so far have taken one single route, there is actually quite a bit of latitude here. The three primary choices are:

Fees go to the validator/miner that created the blockFees go to the validators equallyFees are burned

Arguably, the more salient difference is between the first and the second; the difference between the second and the third can be described as a targeting policy choice, and so we will deal with this issue separately in a later section. The difference between the first two options is this: if the validator that creates a block gets the fees, that validator has an incentive equal to the size of the fees to include as many transactions as possible. If it’s the validators equally, each one has a negligible incentive.

Note that literally redistributing 100% of fees (or, for that matter, any fixed percentage of fees) is infeasible due to “tax evasion” attacks via side-channel payment: instead of adding a transaction fee using the standard mechanism, transaction senders will put a zero or near-zero “official fee” and pay validators directly via other cryptocurrencies (or even PayPal), allowing validators to collect 100% of the revenue. However, we can get what we want by using another trick: determine in protocol a minimum fee that transactions must pay, and have the protocol “confiscate” that portion but let the miners keep the entire excess (alternatively, miners keep all transaction fees but must in turn pay a fee per byte or unit gas to the protocol; this a mathematically equivalent formulation). This removes tax evasion incentives, while still placing a large portion of transaction fee revenue under the control of the protocol, allowing us to keep fee-based issuance without introducing the game-theoretic malicentives of a traditional pure-fee model.



The protocol cannot take all of the transaction fee revenues because the level of fees is very uneven and because it cannot price-discriminate, but it can take a portion large enough that in-protocol mechanisms have enough revenue allocating power to work with to counteract game-theoretic concerns with traditional fee-only security.


One possible algorithm for determining this minimum fee would be a difficulty-like adjustment process that targets a medium-term average gas usage equal to 1/3 of the protocol gas limit, decreasing the minimum fee if average usage is below this value and increasing the minimum fee if average usage is higher.

We can extend this model further to provide other interesting properties. One possibility is that of a flexible gas limit: instead of a hard gas limit that blocks cannot exceed, we have a soft limit G1 and a hard limit G2 (say, G2 = 2 * G1). Suppose that the protocol fee is 20 shannon per gas (in non-Ethereum contexts, substitute other cryptocurrency units and “bytes” or other block resource limits as needed). All transactions up to G1 would have to pay 20 shannon per gas. Above that point, however, fees would increase: at (G2 + G1) / 2, the marginal unit of gas would cost 40 shannon, at (3 * G2 + G1) / 4 it would go up to 80 shannon, and so forth until hitting a limit of infinity at G2. This would give the chain a limited ability to expand capacity to meet sudden spikes in demand, reducing the price shock (a feature that some critics of the concept of a “fee market” may find attractive).

What to Target

Let us suppose that we agree with the points above. Then, a question still remains: how do we target our policy variables, and particularly inflation? Do we target a fixed level of participation in proof of stake (eg. 30% of all ether), and adjust interest rates to compensate? Do we target a fixed level of total inflation? Or do we just set a fixed interest rate, and allow participation and inflation to adjust? Or do we take some middle road where greater interest in participating leads to a combination of increased inflation, increased participation and a lower interest rate?

In general, tradeoffs between targeting rules are fundamentally tradeoffs about what kinds of uncertainty we are more willing to accept, and what variables we want to reduce volatility on. The main reason to target a fixed level of participation is to have certainty about the level of security. The main reason to target a fixed level of inflation is to satisfy the demands of some token holders for supply predictability, and at the same time have a weaker but still present guarantee about security (it is theoretically possible that in equilibrium only 5% of ether would be participating, but in that case it would be getting a high interest rate, creating a partial counter-pressure). The main reason to target a fixed interest rate is to minimize selfish-validating risks, as there would be no way for a validator to benefit themselves simply by hurting the interests of other validators. A hybrid route in proof of stake could combine these guarantees, for example providing selfish mining protection if possible but sticking to a hard minimum target of 5% stake participation.

Now, we can also get to discussing the difference between redistributing and burning transaction fees. It is clear that, in expectation, the two are equivalent: redistributing 50 ETH per day and inflating 50 ETH per day is the same as burning 50 ETH per day and inflating 100 ETH per day. The tradeoff, once again, comes in the variance. If fees are redistributed, then we have more certainty about the supply, but less certainty about the level of security, as we have certainty about the size of the validation incentive. If fees are burned, we lose certainty about the supply, but gain certainty about the size of the validation incentive and hence the level of security. Burning fees also has the benefit that it minimizes cartel risks, as validators cannot gain as much by artificially pushing transaction fees up (eg. through censorship, or via capacity-restriction soft forks). Once again, a hybrid route is possible and may well be optimal, though at present it seems like an approach targeted more toward burning fees, and thereby accepting an uncertain cryptocurrency supply that may well see low decreases on net during high-usage times and low increases on net during low-usage times, is best. If usage is high enough, this may even lead to low deflation on average.