Invited Paper: Further Decentralizing Decentralized Finance: Loss vs Rebalancing Without a Shared Reference Market

Automated market makers (AMMs) typically rely on arbitrage agents to keep prices in line with a shared reference market such as a large centralized exchange. This paper considers an alternative, even-more-decentralized model where prices must stabilize without a shared reference market.We first consider a model where there is one population of AMMs, and another of arbitrage agents who seek to profit from pairwise price differences between randomly-chosen AMMs. For constant-product AMMs, repeated random pair-wise arbitrage causes the AMMs’ expected prices to converge within any precision ϵ > 0 in $\Theta \left( {\max \left( {{n^2}\log n,\log \frac{1}{\varepsilon }} \right)} \right.$ interactions, and arbitrage agents’ profits are proportional to the original price imbalances. Within certain limits, the arbitrage agents can collude to set the final stable price.If, instead, randomly-chosen pairs of AMMs could rebalance their asset pools directly, capturing profits that would have gone to arbitrage agents, then expected AMM prices converge within ϵ with respective upper and lower bounds of $\Omega \left( {\max \left( {{n^2}\log n,\log \frac{1}{\varepsilon }} \right)} \right.$ and $O\left( {\max \left( {{n^2}\log n,\log \frac{1}{\varepsilon }} \right)} \right.$ interactions. Within certain limits, the AMMs can collude to set the final stable price.