I’d like to share with you our recent research around the Uniswap Fee Switch, i.e. the question whether a fraction of trading fees should go to the protocol and UNI token holders.

Some takeaways:

In a perfectly efficient market, the protocol with the lowest take rate (fraction of fees that goes to the protocol) attracts all liquidity. This is an argument against flipping the fee switch.

In a market where a protocol like Uniswap has a “moat” (due to its high profile and brand), the result is different: Assume Uniswap has a fraction of loyal (“sticky”) trade volume, i.e. some users will always trade on Uniswap regardless of price, e.g. because they don’t use or check other DEXs. According to our model, this competitive advantage makes it possible for Uniswap to sustainably introduce a non-zero take rate even when competing with zero take rate competitors. The model also gives some direction on how high to optimally set the take rate.

(Note that, as with every model, simplifying assumptions are made in the paper.)

To be clear, this is not a recommendation for or against flipping the fee switch. Instead, we see this as a first step to providing a basis for making an informed decision whether and how to direct trading fees to the protocol.
We hope our research can be helpful to the Uniswap community. If you have any feedback or suggestions for future research, feel free to reach out, also on Twitter https://twitter.com/robin_ethz.

I agree with you. Facts have proved that if you burn money through web2, you may not be able to occupy the Web3 market. There have been too many cases proving that an excellent token economy model can make the project better developed ~

Yes, indeed. There has to exist a sustainable tokenomic model that generates organic buy pressure for UNI at some point. Otherwise it’ll keep tanking and the treasury won’t be worth anything to further develop the project, which will hurt LPs in the end because liquidity will move to other (more innovative) protocols that can still pay for the cost of development.

I think you’ve done a great job in modeling the basic formulas and dynamics around the fee switch. I’m surprised there aren’t more comments on your work, perhaps you’ve received them outside the forum.

Reading your paper, everything ultimately depends on the values of sticky volumes s1, s2, and the LPs acceptable difference d. These are unknowns for Uniswap before trying out the fee switch in the open. Additionally, I consider d > 0 a fair assumption for practically all pools, since 1) Uniswap is the leader in market share 2) the contracts have been battletested with the most DEX volume.

In terms of describing the real world, the weakness of the model is that it’s fully static in terms of the total trade volume V. You have clearly stated this in the assumptions, but I’d like to emphasize the significance of this on how the model behaves. It ultimately leads to the majority of conclusions from the model to be against the fee switch. The model basically tells how much volume Uniswap would lose by introducing take rates. What if the total volume would start to explode upwards?

Particularly, I believe that activating the fee switch could supercharge Uniswap adoption by generating revenue to own UNI and making everyone more interested in the project.
We are still in the early stages of growing what is possible “the orderbook of the world”.

Therefore, the model could be improved by adding a growth factor g > 0 that depends on the revenue generated to UNI holders. The factor g would affect the total trading volume V, creating a positive feedback loop effect. Then, in addition to the constant cash flow, we could add the future expected growth of the cash flow to the analysis and compare that against the costs now presented in the model (loss of volume/liquidity).

Obviously, this would make the model more complicated but arguably a better one for real world decision making. But once more, really high quality work and a good starting point for further analysis.

Thanks for your feedback. You make some good points, including noting the assumption that the total trade volume is not affected by the take rates.

I personally don’t necessarily see the positive feedback loop you describe.
Instead, considering future volume growth, could also lead to a result more critical of flipping the fee switch.
Future volume could be less sticky than current volume, leading to lower sticky rates. Future trader and liquidity provider could be less loyal towards Uniswap (if some of the loyalty towards Uniswap stems from using it in the past).

Apologies for being a bit late to the party. Thanks for the paper @rfritsch et al! Some comments for you.

What I’m not a fan of

(pg. 3) What are the units for liquidity L1 and L2? Hopefully not TVL, since the analysis is on at least one concentrated AMM. I worry this detail might be especially relevant, since Uniswap’s competitors have different AMM mechanisms. You justify this by saying that V3 is a CPMM for small price ranges, but it’s important to take into account that the ratio of funds-to-depth is incomparable.

I worry that the two-AMM model is a bit unfair in assuming L1+L2 is a constant, since there’s obviously capital flight in times when yields on exchange 1 and 2 go down. Maybe this could be resolved by an alternative liquidity sink L3 whose return profile can be approximated as not depending on the amount of capital deployed to it, like some kind of DeFi risk-free-rate, and then assume that L1+L2+L3 is constant.

Similar to (2), assumption that V is constant is surely false, however it may be fine if you constrained your analysis to talking about market share rather than market size, which seems to be what you’re getting at here.

In aggregate, your assumptions are systematically biased in the direction of underestimating liquidity flight and volume flight that would occur upon introduction of a taker rate.

What I’m a fan of

Interestingly, due to the fact that each assumption seems to be in the direction of over-estimating optimal take rates, you might be able to use your results as an upper bound of optimal take rates.

Your conclusion was perfectly modest, and it’s worded so as to encourage future work. Love this. And the suggestion you give regarding game theory and the repeated taker rate game is excellent. While my intuition is that taker rates are an obvious race-to-the-bottom if there’s 0 sticky liquidity, it’s also obvious that 0 fees is not a Nash equilibrium when sticky liquidity does exist (no matter fees charged, multiply taker rate by the sticky volume and you’re guaranteed to have more exchange revenue than with 0 taker rate). Would love to see (or do?) more research on the stage game and multi-game equilibria here.

Beautiful graphs.

Overall
I think it would be fruitful to reframe the conclusions to provide an upper bound on the exchange-revenue-maximizing taker rate, and I think there’s a straightforward yet illuminating analysis that could be done on the game theory behind multi-stage exchange taker rate wars.

Hi @maxholloway,
thanks a lot for your feedback and suggestions!
The liquidity L1 and L2 are indeed the TVL for v2. For v3, the assumption is that the liquidity is relatively constant in a small range. And for the liquidity one would then choose the TVL as if this liquidity was provided across the whole price range.
Looking forward to seeing any potential future research if you do more in this direction (and feel free to reach out, if you’d like to collaborate)!

I concur. Thanks for the datasheet. Hope models will be implemented to relieve pressure on the token. Also, interface and staking module should be more accessible to lesser tech savy people.

All one has to do is look at Opensea. They are still highly successful with the highest take rate of any market place. They have the brand, marketing, and trust even though they freeze assests, have highest fees, etc.

Hi @rfritsch. In Fig3b and Fig4d, on the left edge of the fig (where t1=0), why is the liquidity share only around 80–85%? Trying to wrap my mind around some math/analytical intuition here Thanks