Paper: arXiv 2301.13009

Authors: Deborah Miori, Mihai Cucuringu

Abstract

Uniswap is a Constant Product Market Maker built around liquidity pools, where pairs of tokens are exchanged subject to a fee that is proportional to the size of transactions. At the time of writing, there exist more than 6,000 pools associated with Uniswap v3, implying that empirical investigations on the full ecosystem can easily become computationally expensive. Thus, we propose a systematic workflow to extract and analyse a meaningful but computationally tractable sub-universe of liquidity pools. Leveraging on the 34 pools found relevant for the six-months time window January-June 2022, we then investigate the related liquidity consumption behaviour of market participants. We propose to represent each liquidity taker by a suitably constructed transaction graph, which is a fully connected network where nodes are the liquidity taker’s executed transactions, and edges contain weights encoding the time elapsed between any two transactions. We extend the NLP-inspired graph2vec algorithm to the weighted undirected setting, and employ it to obtain an embedding of the set of graphs. This embedding allows us to extract seven clusters of liquidity takers, with equivalent behavioural patters and interpretable trading preferences. We conclude our work by testing for relationships between the characteristic mechanisms of each pool, i.e. liquidity provision, consumption, and price variation. We introduce a related ideal crypto law, inspired from the ideal gas law of thermodynamics, and demonstrate that pools adhering to this law are healthier trading venues in terms of sensitivity of liquidity and agents’ activity. Regulators and practitioners could benefit from our model by developing related pool health monitoring tools.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel approach to analyzing Uniswap v3 liquidity by adapting NLP graph embedding techniques (graph2vec) to transaction graphs and formulating an ‘ideal crypto law’ inspired by physics. The empirical methodology is well-structured around a meaningful sub-universe of pools, though long-term out-of-sample robustness remains open for further testing.

Research Flowchart

  flowchart TD
    A[Research Goal: Characterize Uniswap v3 & Liquidity Taker Behavior] --> B[(Input Data: 6,000+ Uniswap v3 Pools, Jan-Jun 2022)]
    B --> C[Workflow: Filter to 34 Trackable Relevant Pools]
    C --> D[Construct Fully Connected Weighted Transaction Graphs for Takers]
    D --> E[Apply Weighted graph2vec Embedding & Unsupervised Clustering]
    E --> F[Outcome 1: Identified 7 Distinct Taker Behavioral Clusters]
    C --> G[Formulate & Test Thermodynamic Ideal Crypto Law]
    G --> H[Outcome 2: Pool Health Monitoring Model for Regulators/Practitioners]