Coexisting Exchange Platforms : Limit Order Books and Automated Market Makers

Automated market makers (AMMs) are algorithms that pool liquidity and make it available to liquidity takers by automatically and algorithmically determining an execution price of a trade. In the recent markets for digital assets, a growing number of blockchain-based decentralized exchanges (DEX) have adopted a general class of AMMs, called Constant Function Market Makers (CFMMs). In this paper, we build a model of coexisting exchanges with two different market-making algorithms: a centralized exchange (CEX) with a traditional limit order book and a DEX with a CFMM. Traders are either informed or uninformed and endogenously choose their trading venue. We first analyze how the arrival of the CFMM affects adverse selection and liquidity on both exchanges. Our result indicates that liquidity on the DEX has a positive spillover effect on that on the CEX. Moreover, we derive the expected return of market makers who provide liquidity via the CFMM algorithm. As in traditional limit-order markets, it constitutes the adverse selection cost of informed trading and a profit from noise trading. We analyze market makers' equilibrium behavior and endogenize the amount of liquidity on the CEX and the DEX