Research on Protocol Fees and Liquidity Incentives

[0x_peter]

Hi, this is Peter Zeitz research fellow at 0x. I’m excited to post some research about economic aspects of our proposal to add fees and liquidity incentives to the 0x protocol. This is something that Amir, Will, Weijie, and I have been working on for a quite a while. So great to finally make this work public.

Abstract:
We are proposing the introduction of an ecosystem fee on the taker side of each 0x trade. The protocol fee will be payable in ETH and the fee amount will be pegged to the gas fee takers pay for inclusion of their transactions in blocks. A portion of the fee revenues generated will be allocated to the 0x community treasury to fund ongoing development of the 0x ecosystem. The remaining fee revenues will be paid out to 0x market makers as a liquidity rebate. The rebate scheme rewards market makers in proportion to a) the amount of liquidity they provide and b) their stake of ZRX tokens. This paper provides a detailed analysis of the fee and rebate scheme’s economic effects on makers, takers, and ZRX holders.

Here is a link to the pdf:
https://drive.google.com/file/d/1Om5oA6Gm-UWkncKxJHmxLNSMgXYAI7rr/view?usp=sharing

[KyleJKistner]

My thought on this is that protocol level fees in order to hedge MMs at the expense of arbitrageurs is an excellent idea that will increase liquidity. However, I believe that the α parameter of the Cobb-Douglas function should be set at α=0 to maximize liquidity for ZRX. The total gain to liquidity that results from hedging MMs is likely to be small to moderate. As you increase the value of α you are funneling those efficiency gains into value capture for the token. There is some (small) value α that keeps the protocol at neutral liquidity relative to the current state. It is possible that raising α too high will actually erode liquidity for the protocol at the expense of value capture.

While I understand the necessity of value capture for the long term sustainability of the protocol, at this early stage I believe liquidity and sustainability are inseparable.

[0x_peter]

Yes Kyle, I agree with you in principle that it is critical to encourage liquidity provision and that returning 100% of fees to MMs would be the most direct way of advancing that goal. It is also important to clarify the protocol’s intended long-term mode of operation. Rebating 100% of revenue to MMs would potentially confuse stakeholders with respect to the intended functionality of ZRX. Thus there is a trade-off between two conflicting objectives here. We aim to strike a balance.

We expect to return a large percentage to MMs. 75% is one possible figure we have discussed. In the near-term, returning 75% of money to MMs may not be enough. To address this, we are exploring the possibility of adding a temporary subsidy to further reward MMs across the board. Expect a post elaborating on these issues in the next 3 to 4 weeks.

In short, we would like to get to the endpoint you are looking for, but plan to use a different path to get there.

Also, thank you for reading the paper so carefully and for the excellent/perceptive feedback!

[KyleJKistner]

It might make sense to quantify exactly how much market makers will be saving by instituting these protocol fees and set α such that the projected value capture funneled to ZRX holders is (substantially) less than that so that the parameter value is empirically grounded.

[0x_peter]

Yes, we are making an effort to do this. However, there is a substantial amount of uncertainty involved in these types of calculations. (We’ll explain in a blog post in 3 or 4 weeks). We will need to collect and analyze data after this is launched to fully characterize its impact on market makers.

[mike_hummingbot]

Great paper - I think the underlying economic model is solid. Found some typos in the paper: treasuty, inutitive, equilbirum, iff

[Zerim]

Enjoyed reading the paper, really thoughtful analysis! I particularly found interesting the use of the concavity property to encourage token holdings to reach an equilibrium.

I have a few points of feedback that I would be interested in getting your thoughts on:

1.) The Discounted Present Value calculation

One benefit of the Cobb-Douglas function is that it makes quantification of the benefits
of ZRX ownership simple. Under this function, ZRX holders receive a fraction (1 − α)
of liquidity rebates in equilibrium.

Suppose that based on some assumptions we
compute that the discounted present value of all current and future liquidity rebates is
X. The present value of the rebate stream accruing to ZRX token holders is then simply
(1 − α) X.

This doesn’t seem correct to me. For one, (1-α) is simply the weight applied to the share of stake in the Cobbs-Douglas function, so doesn’t equal a fraction of the future liquidity rebates. For example, if I haven’t collected any protocol fees directly, all the ZRX tokens in the world wouldn’t entitle me to any rebate fees.

Secondly, it doesn’t obvious to me that this scheme should capture any additional value in ZRX token. If, at equilibrium, we could expect all makers to get 100% of the protocol fee attributed to them back as a rebate, then in the absence of some other price floor, I would expect makers to adjust the maker fee such that when taken in conjunction with the expected protocol fee (taking into account the opportunity cost of waiting on the rebate), that they would turn normal profits.

If the ZRX token already had exogenous value, then I would expect makers to charge a fee to which accounts for this opportunity cost and once again turn normal profits, but I wouldn’t expect the protocol fee to be a source of value capture.

2. Maker profit calculation.

In Formula 5, you show the following:

Shouldn’t the theta term just be the portion of theta that goes to the protocol fee? (It was defined earlier as the mean maker profits, including the maker fee and the protocol fee).

Also, what is c and 1-c doing in this equation? This was defined earlier as the expectation of the maker as to how their income would be divided, but it seems to me that profits would be wholly defined by the z_it and l_it terms, reflecting the maker’s budgeting decisions.

3. Does this punish token holders for not forecasting correctly?

If makers must commit their stake at the beginning of a three month epoch, then they will be penalized on their inability to accurately forecast their personal protocol fee contribution to the rebate pool, as well as the aggregate contributions to the rebate pool by the rest of the network.

Apologies if these seem like nitpicks, the paper touched on some things I’m thinking deeply about right now, so felt inclined to get in the weeds.

Looking forward to your response!