Game Theoretic Liquidity Provisioning in Concentrated Liquidity Market Makers

Automated market makers (AMMs) are decentralized exchanges (DEXes) that allow users to exchange cryptocurrency via a smart contract that algorithmically manages liquidity and exchange rates [53]. As a dominant class of DEXes [20], AMMs play an outstanding role more generally as decentralized applications [15]. Today, AMMs drive billions of dollars in daily trading volume on several blockchains [19, 34].

The core functionality of AMMs is facilitated by liquidity pools, i.e., blockchain smart contracts that store and manage cryptocurrency tokens for trading. Most liquidity pools store two types of tokens, which we denote 𝑋 and 𝑌; we focus on the two-token class of AMMs in this work. Atypical trade proceeds in three steps:

(a) A trader proposes to pay Δ𝑥 amount of the 𝑋 token and asks for a quote.

(b) The pool tells the trader they will obtain Δ𝑦 amount of the 𝑌 token (assuming there is sufficient liquidity in the pool).

(c) The trader decides whether to execute the token swap, in which case they also must pay a trading fee (in units of 𝑋) that is proportional to the amount of added tokens.