skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Composing Networks of Automated Market Makers
Automated market makers (AMMs) are automata that trade electronic assets at rates set by mathematical formulas.AMMs are usually implemented by smart contracts on blockchains. In practice, AMMs are often composed: trades can be split across AMMs, and outputs from one AMM can be directed to another. This paper proposes a mathematical model for AMM composition. We define sequential and parallel composition operators for AMMs in a way that ensures that AMMs are closed under composition, in a way that works for “higher-dimensional” AMMs that manage more than two asset classes, and so the composition of AMMs in “stable” states remains stable.  more » « less
Award ID(s):
1917990
PAR ID:
10300608
Author(s) / Creator(s):
;
Date Published:
Journal Name:
ACM Advances in Financial Technologies
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Guruswami, Venkatesan (Ed.)
    In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to characterize and interpret the optimal (i.e., profit-maximizing) strategy of a monopolist liquidity provider, as a function of that LP’s beliefs about asset prices and trader behavior. We introduce a general framework for reasoning about AMMs based on a Bayesian-like belief inference framework, where LPs maintain an asset price estimate, which is updated by incorporating traders' price estimates. In this model, the market maker (i.e., LP) chooses a demand curve that specifies the quantity of a risky asset to be held at each dollar price. Traders arrive sequentially and submit a price bid that can be interpreted as their estimate of the risky asset price; the AMM responds to this submitted bid with an allocation of the risky asset to the trader, a payment that the trader must pay, and a revised internal estimate for the true asset price. We define an incentive-compatible (IC) AMM as one in which a trader’s optimal strategy is to submit its true estimate of the asset price, and characterize the IC AMMs as those with downward-sloping demand curves and payments defined by a formula familiar from Myerson’s optimal auction theory. We generalize Myerson’s virtual values, and characterize the profit-maximizing IC AMM. The optimal demand curve generally has a jump that can be interpreted as a "bid-ask spread," which we show is caused by a combination of adverse selection risk (dominant when the degree of information asymmetry is large) and monopoly pricing (dominant when asymmetry is small). This work opens up new research directions into the study of automated exchange mechanisms from the lens of optimal auction theory and iterative belief inference, using tools of theoretical computer science in a novel way. 
    more » « less
  2. ; ; (, arXiv preprints)
    Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using automated market makers (AMMs). Specifically, we construct a liquidity-based AMM structure for prediction markets that, under reasonable axioms on the underlying utility function, satisfy meaningful financial properties on the cost of betting and the resulting pricing oracle. Importantly, we study how liquidity can be pooled or withdrawn from the AMM and the resulting implications to the market behavior. In considering this decentralized framework, we additionally propose financially meaningful fees that can be collected for trading to compensate the liquidity providers for their vital market function. 
    more » « less
  3. ; ; (, arXiv preprints)
    Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using automated market makers (AMMs). Specifically, we construct a liquidity-based AMM structure for prediction markets that, under reasonable axioms on the underlying utility function, satisfy meaningful financial properties on the cost of betting and the resulting pricing oracle. Importantly, we study how liquidity can be pooled or withdrawn from the AMM and the resulting implications to the market behavior. In considering this decentralized framework, we additionally propose financially meaningful fees that can be collected for trading to compensate the liquidity providers for their vital market function. 
    more » « less
  4. ; ; (, Financial Cryptography)
    We consider the impact of trading fees on the profits of arbitrageurs trading against an automated marker marker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to both introduce fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of time that an arriving arbitrageur finds a profitable trade. 
    more » « less
  5. ; ; ; ; (, Proceedings of the ACM on Measurement and Analysis of Computing Systems)
    Automated marker makers (AMMs) are decentralized exchanges that enable the automated trading of digital assets. Liquidity providers (LPs) deposit digital tokens, which can be used by traders to execute trades, which generate fees for the investing LPs. In AMMs, trade prices are determined algorithmically, unlike classical limit order books. Concentrated liquidity market makers (CLMMs) are a major class of AMMs that offer liquidity providers flexibility to decide not onlyhow muchliquidity to provide, butin what ranges of pricesthey want the liquidity to be used. This flexibility can complicate strategic planning, since fee rewards are shared among LPs. We formulate and analyze a game theoretic model to study the incentives of LPs in CLMMs. Our main results show that while our original formulation admits multiple Nash equilibria and has complexity quadratic in the number of price ticks in the contract, it can be reduced to a game with a unique Nash equilibrium whose complexity is only linear. We further show that the Nash equilibrium of this simplified game follows a waterfilling strategy, in which low-budget LPs use up their full budget, but rich LPs do not. Finally, by fitting our game model to real-world CLMMs, we observe that in liquidity pools with risky assets, LPs adopt investment strategies far from the Nash equilibrium. Under price uncertainty, they generally invest in fewer and wider price ranges than our analysis suggests, with lower-frequency liquidity updates. In such risky pools, by updating their strategy to more closely match the Nash equilibrium of our game, LPs can improve their median daily returns by $116, which corresponds to an increase of 0.009% in median daily return on investment (ROI). At maximum, LPs can improve daily ROI by 0.855% when they reach Nash equilibrium. In contrast, in stable pools (e.g., of only stablecoins), LPs already adopt strategies that more closely resemble the Nash equilibrium of our game. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email