Excited to release a new paper with @davidecrapis! We present a game theoretic model of simultaneous liquidity provision by passive LPs. We show that competition between liquidity providers causes a loss in total LP welfare that grows linearly with the number of passive LPs.

ethereum protocol research /ethrd + Crypto x AI /dacc 

Passive LPs have two reasons to deposit liquidity. More liquidity induces more trading demand, and leads to a greater share of total fee revenue, since fee revenues are distributed proportional to the fraction of liquidity provided. The liquidity and competition effect

Our main result is that the price of anarchy, defined over the liquidity provider performance, is O(N), meaning that the welfare loss to LPs scales linearly with the number of passive LPs

Finally, we show that clever AMM design may reduce the arbitrage intensity per unit of liquidity but that this does not lead to a proportional decrease in the total amount of arbitrage and, under some circumstances, even an increase.

The intuition is that as the arbitrage intensity per unit of liquidity decreases, more liquidity flows in, so the total amount of arbitrage may not decrease proportionally.

For the full paper, see https://arxiv.org/abs/2402.18256

These two effects are not aligned because the marginal LP tries to get some of the fee revenue obtained in the AMM without this additional liquidity. This means that LPs deposit liquidity beyond the optimal point: where fee revenues equals adverse selection and opportunity costs