# RPL incentives for rETH/ETH liquidity on uniswap v3

tldr; RPL annual inflation required is very likely under 2%

Uniswap v3 is an orderbook. We only need limit orders that buy rETH (possibly at discount). We do not need limit orders that sell rETH as people who want to market buy rETH can deposit into rocketpool instead.

Assume Rocketpool has total X ETH deposited assigned to validators. About 0.5X backs rETH and 0.5X belongs to validator owners. Assume RPL market cap is Y ETH. By necessity, Y > 0.05X, so X/Y < 20

`As of today, X = 22k, Y = 180k. Y is not just greater than 0.05X, it is even greater than X.`

Assume we want r fraction of rETH to able to exit their positions at any given moment.

`For example if 10% of rETH holders should be able to exit then take r = 0.10`

Assume we need to pay the ETH single-sided LP y yield per year. (measured as fraction of ETH). Not that this ETH is not locked, so the yield to be paid may be less than staking yield, in fact it will be comparable to DeFi yields. Staking yield likely acts as an upper bound on how much yield has to be paid.

`For example if DeFi yield right now is 0.5% on ETH and we have to pay 2% annual then take y = 0.02`

Then we need to pay `0.5 * X * r * y` annual. RPL annual inflation required is `0.5 * X * r * y / Y`

#### Calculations

Today
X = 22k, Y = 180k, r = 0.1, y = 0.02
RPL annual inflation = 0.000012 = 0.0012%

Long-term realistic
X/Y = 4, r = 0.1, y = 0.02
RPL annual inflation = 0.004 = 0.4%

RPL stake worst case
X/Y = 20, r = 0.1, y = 0.02
RPL annual inflation = 0.02 = 2%

rETH freedom-to-exit worst case
X/Y = 4, r = 0.5, y = 0.02
RPL annual inflation = 0.02 = 2%

Absolute worst case
X/Y = 20, r = 0.5, y = 0.04
RPL annual inflation = 0.20 = 20%

#### But what if there are sells?

We have assumed there is ETH sitting in uni v3 LP waiting to be sold into, and it earns RPL incentives. We haven't considered what happens if someone actually sells rETH into the ETH.

Need to figure out what exchange rates are likely and what to incentivise.

Two reasons for sells:
- Liquidations
- rETH investor wants to exit early

For liquidations, signifcant penalty is acceptable. For instance rETH trading at 3-5% discount to underlying ETH deposit. A person getting liquidated can afford to lose a year's worth of yield.

For rETH investors, this is not acceptable, they will want to pay a much smaller discount for earlier exits. Possibly even zero discount.

For an LP who does not mind the lockup associated with holding rETH, they will be okay with offering smaller penalty on rETH/ETH. But then they will also find the higher yield of holding rETH attractive, as compared to holding ETH inside rETH/ETH LP and hoping someone sells into it, while earning possibly lower yield.

Worst case is LP needs to be paid the full 5% in RPL incentives that rETH holders earn (r = 0.05).