An analysis of Uniswap markets

So reading through this I take away two main things:

  1. Convex equations allow for DEXs to operate using relatively simple math, and by utilizing these computationally efficient equations they can increase the security of their liquidity pools by ensuring the LPs cannot be fully depleted with just one trading pair.
  2. Prices may be highly impacted by small liquidity pools/reserves when CPMs are used.

The second takeaway is the one I want to focus on. The authors state in the paper:

…the price is likely to be less stable in the case of smaller reserves (pg8)

I recently posted another research summary here discussing AMMs where the author made a similar statement regarding constant product markets when reserves are low:

…the token price could range from 0 to ∞ in the constant product cost model, when the price for one token is close to infinity, any meaningful trade in the market is infeasible.

Given both researchers, and many others, have concluded constant product makers may be sensitive to low reserves (when one asset’s reserves approach 0 the price should increase towards ∞ given the CPM) has Uniswap, or other DEXs, put in mechanisms to ensure or encourage relatively large reserves?

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