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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
1. Minimum viable issuance is an important principle in staking economics. This thread will further advance the concept by analyzing how issuance level affects Ethereum’s equilibrium staking conditions, guiding us to a utility-maximizing reward curve. https://notes.ethereum.org/@anderselowsson/MinimumViableIssuance
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
2. This thread is 116 tweets long and has 32 figures, so I am here linking to it as a post as well. There is a second part forthcoming and I will also provide an ethresearch post covering the topic shortly for those more comfortable with that format. https://notes.ethereum.org/@anderselowsson/HyUIqjo_6
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Anders Elowsson
@anderselowsson
3. Before I start I would like to thank @barnabe, @fradamt, @vitalik.eth, @soispoke and @justindrake for fruitful discussions and feedback for this thread, as well as @ansgar.eth, @davidecrapis, @caspar and @julianma for fruitful discussions. I also wish to thank Flashbots for providing the data used for this analysis.
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Anders Elowsson
@anderselowsson
4. The demand curve shifted upwards after The Merge when stakers started to receive MEV and priority fees. Reservation yields fell after Shapella due to improved liquidity, and the supply curve shifted downwards. Both changes pushed up the equilibrium quantity of stake.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
5. Because of this, Ethereum has arguably entered a phase of overpaying for security. To what extent can we stop overpaying? Can we reduce issuance while still retaining consensus stability, proper incentives, and acceptable conditions for solo staking?
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
6. Can we adopt a reward curve that lets the issuance yield go negative past some specific staking deposit size D, or target some specific desirable D by simply adapting the yield to enforce it? Otherwise, should a more moderate approach be adopted?
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
7. We will take a closer look at these questions and review features of staking economics that affect consensus incentives and reward variability—including how they vary across deposit size. This will guide our approach to minimum viable issuance (MVI).
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
RELATIONSHIP BETWEEN THE EQUILIBRIUM STAKING AND F 8. The base reward factor F is the big knob for adjusting the total issuance level under the current reward curve. It affects all consensus rewards and penalties and provides an issuance yield under idealized performance of y_i=cF/D^0.5. The constant c is around 2.6.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
9. The total yield provided by the protocol to stakers implies its demand for stake and it is y=y_i+y_v, where y_v is the yield from realized extractable value (REV). Denote yearly REV as V (currently around 300k ETH). We then have y_v=V/D.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
10. Note that y is the endogenous yield derived exclusively from staked participation in the consensus process. Yield from DeFi/restaking that is exogenous to staking is not modeled here; it can under competitive equilibrium also be derived by non-stakers. https://x.com/weboftrees/status/1710720809797407063
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Anders Elowsson
@anderselowsson
11. The colormap and y-axis both capture y, with the colormap restricted to F=0-75. Currently, F=64. At equilibrium, the demand curve will intersect the supply curve that captures how prospective ETH holders’ inclination to stake varies with yield.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
12. The shape of the supply curve is unknown. The two examples in blue have a yield elasticity of supply of 2, with the lower also used in the last thread. Plots will be provided covering a broader range so that different assumptions can be mapped to various outcomes. https://x.com/weboftrees/status/1710706011185545671
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
13. The upper curve could for example represent the supply curve underpinning a medium-run equilibrium (within a year or two), whereas the lower curve could be the supply curve after a few years of improvements to the the staking experience and better financial integrations.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
14. The left dashed blue line indicates the revealed preference of The Merge at D=14M ETH. By staying to the right of this line, we are operating at a deposit size that has been previously regarded as sufficiently safe by the Ethereum community. https://x.com/weboftrees/status/1710717027520831749
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
15. The right dashed line indicates 2^25 ETH (33.6M ETH), which has been used as a reference point capturing when network conditions (and economics) start to degrade. By staying to the left of the line, Ethereum is better positioned on these issues. https://notes.ethereum.org/@vbuterin/single_slot_finality
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Anders Elowsson
@anderselowsson
16. Potential equilibria under the current issuance policy (F=64) and REV are indicated by blue circles, and the equilibria if issuance is halved (F=32) are indicated by blue squares. Such a reduction brings the deposit size closer to a previously suggested desirable range.
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Anders Elowsson
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17. It is not possible to ascertain the exact effect of a reduction in F, but we can be rather certain that the yield elasticity of supply for the medium run is not 0 (a vertical supply curve). Reducing F will therefore always reduce the quantity of stake, ceteris paribus.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
18. Note that the full reduction in yield from a change in F (white downwards arrow) will not remain at the new equilibrium, because some stakers will presumably leave (blue leftwards arrow), bringing the yield for remaining stakers back up a bit (white leftwards arrow).
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
19. For the specified supply and demand curves, the equilibrium yield initially falls from 2.89% to 1.74% when reducing F from 64 to 32 (a reduction of around 2/5), but then comes back up to 2.33% as some stakers leave. The equilibrium yield is thus reduced by around 1/5.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
20. How will this dynamic affect the solo staker and delegating staker? The outcome over shorter time horizons will depend on variations in cost structures and frictions affecting the decision to stake or de-stake.
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Anders Elowsson
@anderselowsson
21. A solo staker who will not buy new hardware at some low yield may still stake over the lifetime of their current hardware. Delegating stakers dissatisfied with the yield may keep their savings in the LST until the next time they wish to spend their money, or leave directly.
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Anders Elowsson
@anderselowsson
22. Solo stakers’ upfront costs and illiquidity presumably give them a lower yield elasticity of supply in the short run. This is comforting, because a temporarily lower-than-equilibrium yield (if F is reduced in a hard fork) may not push them out forever. https://x.com/weboftrees/status/1710719952968106177
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Anders Elowsson
@anderselowsson
23. It seems likely that the supply curve will gradually shift downwards over time as the staking experience simplifies and DeFi integrations improve. The outlined dynamic in §18 may therefore not fully materialize, as a lowering supply curve can nullify any de-staking process.
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Anders Elowsson
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24. The equilibrium quantity of stake will however still be lower with a reduction in F than if F is kept fixed. We must evaluate each possible outcome at the medium-run equilibrium. The effect of a gradually lowering supply curve is a gradually increasing deposit size/ratio.
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Anders Elowsson
@anderselowsson
25. This figure has F on the y-axis instead of yield. You may think of it as dragging down and straightening the bent colormap in §11 such that it becomes a rectangle. The colors encode the same yield as previously (also indicated by black lines).
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
26. This viewpoint is convenient as we will now further explore the effect of a change to the issuance level. We will often provide both alternative graphs to the reader and indicate the same two supply curves as guidelines.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
INCENTIVE STRUCTURE 27. When contemplating a change to the issuance policy, it is important to consider the effects on consensus stability, in particular how incentives may change for different consensus roles that validators will be assigned to.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
28. This figure shows the expected rewards stemming from issuance at various settings for the base reward factor F. The hypothetical equilibria are once again indicated. Naturally, the lower F is set, the lower the proportion of rewards that come from issuance.
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Anders Elowsson pfp
Anders Elowsson
@anderselowsson
29. Right now at the prevailing level of REV, more than 2/3 of rewards come from issuance. Since y_v changes by the reciprocal of D whereas y_i changes by the reciprocal of D^0.5 under the current reward curve, a higher proportion of rewards will stem from issuance at a higher D.
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