A growing number of blockchain-based decentralized exchanges (DEX) have adopted Constant Function Market Makers (CFMMs)—a single-function algorithm to determine the execution price for a trade. We build a model of coexisting exchanges where a centralized exchange (CEX) with the traditional order-book mechanism operates in parallel with a DEX with the CFMM. Traders are either informed or uninformed and endogenously choose their trading venue. We first investigate how the arrival of the CFMM affects an adverse selection cost for market makers and liquidity on both exchanges. Our result indicates that liquidity on the DEX has a positive spillover effect on CEX liquidity. Secondly, we derive a profit function for liquidity providers using the CFMM when there is an asymmetric information problem. As in the traditional market microstructure theory, informed trading imposes an adverse selection cost, while uninformed noise trading adds value to liquidity pools. We analyze the market makers’ equilibrium behavior and endogenize the amount of liquidity supplied via the CFMM. 

Key words: Automated Market Makers, Constant Function Market Makers, DeFi, decentralized exchanges, Uniswap, limit order book, market liquidity, asymmetric information