Abstract
A growing number of blockchain-based decentralized exchanges have adopted automated market makers to attract liquidity, and they replace the traditional order book system for trade execution. This paper studies the equilibrium liquidity provision via constant product market makers, one of the simplest and widely adopted algorithms of automated market making. The model derives the optimal behavior of liquidity providers and the aggregate size of the liquidity pool on a constant product market. As suggested by the traditional market microstructure literature, I demonstrate that information asymmetry between traders leads to an adverse selection problem and plays a key role in determining equilibrium liquidity on an automated market. Moreover, when liquidity providers are strategic, I find that competition between them exhibits both strategic substitution and complementarity, making the best response function of each liquidity provider non-monotonic in her rivals' liquidity supply. The model also shows that the equilibrium market liquidity tends to be stable and does not diverge or evaporate even if a (small) temporary shock hits the market.
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