This EIP research post provides the rationale for adjusting Ethereum’s issuance policy to use a reward curve with tempered issuance. It covers relevant trade-offs, reviews security considerations, and discusses the endgame.

This EIP research post provides the rationale for adjusting Ethereum’s issuance policy to use a reward curve with tempered issuance. It covers relevant trade-offs, reviews security considerations, and discusses the endgame. https://ethresear.ch/t/reward-curve-with-tempered-issuance-eip-research-post/19171

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It simply divides the current reward curve by 1+D/k where D is deposit size, and k automagically comes to define the quantity staked at the peak issuance point (plus sign), which also becomes the point where issuance is halved relative to the current reward curve.

A graduated approach is preferable, because it provides time for stakers to adapt before a full reduction takes place, smooths out disequilibria, and allows for an intermediate evaluation of effects on the composition of the staking set as well as the equilibrium quantity staked.

Staking yield under the current level of MEV is here shown. The blue lines are just future hypothetical supply curves, that may shift downwards, increasing the quantity staked and decreasing the yield. The dashed curve represents a graduated approach intended for the next fork.

The analysis begins by reviewing the effect that issuance policy has on user utility. It is important to understand that a high issuance level compels users to incur higher costs than necessary. The area below the supply curve is the implied aggregate cost to stakers and the area above represents their surplus.

Relevant costs include hardware and other resources, upkeep, the acquisition of technical knowledge, illiquidity, trust in third parties and other factors increasing the risk premium, various opportunity costs, taxes, etc. The proposal reduces costs corresponding to the darker blue region, and welfare improves.

Too often, all staking yield is considered as a surplus, with the implication that issuance policy is a zero-sum game. But due to implied costs, corresponding to issuance that does not generate any surplus to stakers, issuance policy is *not* zero sum.

To illustrate this, the attainable change to someone’s proportion of all ETH can be calculated as

y_p = (1+y)/(1+s)-1.

It can be interpreted as the Fisher equation adapted to Ethereum. This “proportional yield” can be computed for both stakers and non-stakers, in the latter case with y=0.

The figure compares y_p at two equilibria, through the associated changes to y and s. When changing from the current reward curve to the proposed reward curve, stakers are left virtually unaffected, whereas both non-stakers and de-stakers benefit (treating de-stakers' reservation yield as an indifference point).

The post then discusses the macro perspective, following my previous analysis. The macro perspective is very important and a broad topic but has already been given much attention lately, I will just share how I tried to sell it to Justin last summer.

The post then discusses the macro perspective, following my previous analysis. The macro perspective is very important and a broad topic but has already been given much attention lately, I will just share how I tried to sell it to Justin last summer. https://x.com/weboftrees/status/1710710993989316652?s=20

Section 4.2 reviews how the staking yield may affect the proportion of solo stakers under equilibrium. The biggest risk to solo-staking viability is economies of scale. But if an issuance policy leads to more staking, dominant SSPs can offer lower fees, better LST money, and lower risk due to emerging moral hazard.

We must also remember that self-custody is an important paradigm for many users and that LSTs come with risks; this will affect the supply side of the analysis. A problem of a high issuance level is that it forces a principal—agent problem on more unsophisticated users that do not wish to see their savings eroded.

At a fundamental level, the conjecture is that the relative distribution of reservation yields may differ between different classes of stakers. This then leads to different proportions of solo stakers at different quantities staked. But whether one policy is better than the other cannot be ascertained.

To balance trade-offs, the proposed reward curve offers a positive yield across the full range—low enough to make a high quantity stake unlikely, yet sufficiently high as to never force out solo stakers on reasonably efficient setups.

A scenario with a very suppressed supply curve is analyzed as shown in the figure. Although it may seem improbable with such a low supply curve, it is important to understand what would happen in more improbable scenarios. With the proposed reward curve in green, the staking yield becomes 1 %.

Ethereum can fundamentally be designed to enforce an equilibrium at any point along the supply curve. Would an equilibrium at the blue star corresponding to 30M ETH staked and 0.37 % yield be better? Approaches that enforce a low quantity stake might make conditions for solo staking particularly unappealing.

An upward shift to the equilibrium quantity of stake—from the blue star to the green circle—acts as a “safety valve”, which helps Ethereum neutralize the less desirable properties of a low quantity of stake under a lower supply curve.

The consensus mechanism essentially absorbs all delegating stakers with low reservation yields, just to push up the yield enough for solo stakers to still operate a validator at a profit. Regardless of whether this is desirable or not, for the sake of users, the upward shift must *only* take place if strictly required.

This is something that the reward curve facilitates. Would stakers prefer the equilibrium for the current reward curve at the black square instead in the last figure? The issuance level at the black square is around 1.7M ETH per year, i.e., almost four times higher than under the proposed curve.

Therefore, even though the yield increases by almost 1 %, the supply inflation rate increases even more. Thus, remarkably, stakers are worse off under the current reward curve than under the proposed reward curve.

This figure shows an “isoproportion map”, where thin black lines indicate “isoproportion lines” along which stakers’ proportional yield stays the same. If the supply curve is steeper than the associated isoproportion line, stakers benefit from an increase in issuance, if it is flatter, they are worse off.

The blue-white isoproportion line of the equilibrium at the black square is steeper than the hypothetical supply curve. Therefore, stakers benefit from a reduction in issuance.

The post takes a closer look at discouragement attacks and cartelization attacks in Section 5.3-4. The proposed reward curve has been designed to incorporate a sufficiently small issuance reduction so as to not exacerbate the risks of these attacks.

Section 6.3 explores the endgame. The proposed reward curve can be viable for a long time, perhaps forever. The analysis does not try to assert that it *must* remain in place indefinitely, just that it makes a rather suitable endgame, with clear improvements over the current curve.

The post concludes by broadening the utility measure for token holders to incorporate the development of the entire ecosystem, by cautioning against exploiting users' bounded rationality concerning yield, and to urge the community to take a step in the right direction.

I designed this reward curve to moderate quantity staked while still maintaining reliable consensus incentives, economic security, resistance to discouragement attacks and cartelization attacks, a favorable composition of the staking set, and viable conditions for solo staking.