Arbitrage in automated market makers

One of the most interesting applications of blockchain is given by the automated market makers (AMMs). In the paper, we discuss how arbitrage activity between the AMMs and the other exchange nodes can affect the volumes of assets in liquidity pools of constant function AMMs. In particular, we argue that arbitrage superimposes to the constant function in determining the liquidity volumes within the same AMM and across different AMMs. Yet, despite representing an additional condition in the model, equilibrium arbitrage is typically not unique because it may depend on several elements, such as the amount of liquidity in the system and the number of exchange nodes. Hence, the paper discusses how the constant function and arbitrage jointly determine the relationship across the assets’ liquidity volume in the pool but not a unique value for such volumes unless further constraints are introduced. Therefore, a platform interested in predicting the pool’s liquidity volumes may face indeterminacy as to which equilibrium would prevail. Though arbitrage has been discussed in related literature, equilibrium indeterminacy does not seem to have been pointed out.