The Case for Variable Fees in Constant Product Markets: An Agent Based Simulation

We are interested in how the relationship between the fee in a constant product market (CPM) and the volatility of the swapped pair on other liquid exchanges influences the losses/gains of the liquidity providers. We review three classical market making models: Glosten and Milgrom, Kyle and Grossman and Miller and note that these very different models there is always a relationship between volatility and how rational market makers set prices. Motivated by this we set up an agent based model to explore this in the context of CPMs like Uniswap. We conclude that if the fee is too low relative to the volatility of the traded pair then the liquidity providers will end up making a loss over the medium term. From this we go to suggesting that CPM markets need to let liquidity providers set the fee via a governance mechanism especially as volatilities of assets fluctuate.