Properties of issuance level: consensus incentives and variability across potential reward curves

First I would like to note that the cited section strictly refers to the effect in the short run of solo stakers operating on longer time horizons. You are correct that this is a different topic than the topic of retaining solo stakers in the long run, which is why I deal with it in different sections here (2.2 and 5.4). The reason for mentioning the short run is that the impact of a change in issuance policy can be a temporarily-lower-than-equilibrium yield (as specifically depicted in Figure 3), and it is important to understand its effect.


The complex conundrum of retaining solo stakers

Ethereum wants to retain solo stakers, at least when measured as a proportion of all stakers. The expected outcome of a reduction in issuance level is a lower equilibrium quantity of stake among both delegating and solo stakers. Using Figure 3 as an example, one question is if the proportion of solo stakers is lower at around 33M ETH staked and a staking yield of 2.34 % than at around 50M ETH staked and a staking yield of 2.95 %. The concern is if there may be a staking yield below which solo stakers in particular would drop off due to the higher costs associated with solo staking. If solo stakers leave en masse below a yield of 2.5 % (while some substitute as you suggest), then a staking yield of 2.34 % at 33M ETH staked may give a lower proportion than when the yield is 2.95 % at 50M ETH staked. This is of course something to take seriously.

There are however also some arguments for why a more restrictive reward curve could give a higher or at least similar proportion of solo stakers (I will refer directly to relevant sections from my thread on minimum viable issuance):

So while the concern is valid, there are also some nuances to it. There are also arguments that pertain more specifically to the medium run than the last bullet-point, but may not pertain to the very long run. It is for example less probable that solo stakers labeled as solo stakers give up their validator during the next few years, while such labels hold merit and more valuable airdrops can be expected. We are currently in the transition to single-slot finality, and the consensus mechanism may change going forward [1, 2]. So keeping an eye on the medium run is still somewhat relevant, since a consensus update may substantially alter the equation anyway for the long run. Still, arguments pertaining to the medium run are not and should not be the core part of the reasoning, because this could lead us wrong over the long run.

The slope of the supply curve will of course greatly influence the difference in yield and deposit size under two different issuance policies. A flatter curve may produce a very small difference in yield between the two equilibria, even if one policy has a much more restrictive reward curve. A steeper supply curve can give a somewhat bigger difference, but a comparison cannot be made strictly across the same deposit size between two reward curves. It is important to note that the supply curve will slope upward. Allowing the quantity of stake to expand if the supply curve is very low thus acts as a "safety valve", ensuring some reasonable yield for solo stakers also under such circumstances (as well as ensuring a more manageable variability and retained consensus incentives as previously specified). This helps explain why it would be undesirable to be “dogmatic”, and pursue a negative yield at lower deposit sizes.

There is also another variable that I would like to highlight, which is important to remember when we seek to understand the rationale behind, i.e., the candidate reward curve, and why we still wish to be more restrictive than the current reward curve in our balancing act. That variable is REV, and the fact that it can vary going forward. Thus it is not only the supply curve that we must take a probabilistic approach to, but also the demand curve. We can review Figure 39 and the yield the candidate reward curve offers at 110M ETH staked. The expected staking yield there is only 0.65 %. At the current token price of around $2800, a 32 ETH stake then only gives an expected monthly income of $50. The “guaranteed” attestation rewards not deriving from block proposal or sync-committee duties are only half of that. Clearly this is a rather low income if you only stake with one validator.

However, a reasonable prior for the supply curve is that the yield must be quite a bit higher than 0.65 % for as much as 110M ETH to get staked. The only time an equilibrium can be expected at 110M ETH staked is thus if the REV increases significantly, pushing up the staking yield to required levels (at which point the increased penalties suggested by Buterin would come in very handy). The low issuance yield thus pre-emptively counters a higher REV (the staking yield will never go lower than what is stipulated by the supply curve under equilibrium). And of course, the low issuance yield at the maximum deposit size is motivated in the first place by how undesirable it would be with this high quantity of stake from the perspective of network load and economics.

In conclusion, your argument (and similar) pertaining to solo stakers is valid and good to bring forward, but there are important counterarguments as well. This is a “complex conundrum” that must be evaluated under equilibrium. We must even allow our priors regarding the supply curve and REV to influence the reasoning, given the probabilistic nature of many variables. I will return with a more extensive and formal write-up on the matter. It is important to remember that we optimize for many variables here, and must seek to find a solution that works well under many different scenarios, while trying to temper the growth in the quantity of stake. I believe that the candidate reward curve is rather suitable in this regard.