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.
- 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
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
l_it terms, reflecting the maker’s budgeting decisions.
- 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!