Modeling Arbitrage with an Automated Market Maker

Automated Market Makers (AMMs) are a relatively new mechanism that allow people to trade cryptocurrencies instantly. Unlike typical centralized trades that utilize order-books, AMMs are decentralized, so they do not require the matching of buyers and sellers for exchanges; rather, they use a pre-determined formula to offer prices for trades. AMMs have recently gained popularity within the blockchain ecosystem, with the value of cryptocurrencies locked in decentralized finance reaching 89.23 billion USD; however, AMMs remain relatively unstudied by economists. This paper provides an introductory analysis of AMMs through agent-based modeling, using the mTree Microeconomic Systems framework. Utilizing the framework, we model a decentralized finance environment, blockchain and AMM institutions, and different agent types, incentivized to trade for various reasons. With computer simulations, different behaviors of agents using AMMs and different characteristics of AMMs are modeled as treatments and run numerous times. We specifically analyze arbitrage agents, a trader-type who uses token price differences in various markets to make low-risk profits and equilibrate the prices of cryptocurrencies across markets. Since arbitrage agents have not been studied through simulations, we provide the first analysis of arbitrage activity using this method and explore how their behavior can influence an AMM’s efficiency. We find that an AMM’s liquidity depth impacts the performance of agents and the volatility of prices, indicating that this, and other features should be considered when using and creating AMMs