A theory of Automated Market Makers in DeFi

Massimo Bartoletti; James Hsin-yu Chiang; Alberto Lluch-Lafuente

doi:10.46298/lmcs-18(4:12)2022

Massimo Bartoletti ; James Hsin-yu Chiang ; Alberto Lluch-Lafuente - A theory of Automated Market Makers in DeFi

lmcs:8955 - Logical Methods in Computer Science, December 19, 2022, Volume 18, Issue 4 - https://doi.org/10.46298/lmcs-18(4:12)2022

A theory of Automated Market Makers in DeFiArticle

Authors: Massimo Bartoletti ; James Hsin-yu Chiang ; Alberto Lluch-Lafuente

Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. AMMs allow users to trade different types of crypto-tokens, without the need to find a counter-party. There are several implementations and models for AMMs, featuring a variety of sophisticated economic mechanisms. We present a theory of AMMs. The core of our theory is an abstract operational model of the interactions between users and AMMs, which can be concretised by instantiating the economic mechanisms. We exploit our theory to formally prove a set of fundamental properties of AMMs, characterizing both structural and economic aspects. We do this by abstracting from the actual economic mechanisms used in implementations, and identifying sufficient conditions which ensure the relevant properties. Notably, we devise a general solution to the arbitrage problem, the main game-theoretic foundation behind the economic mechanisms of AMMs.

https://doi.org/10.46298/lmcs-18(4:12)2022

Source: arXiv.org:2102.11350

Volume: Volume 18, Issue 4

Published on: December 19, 2022

Accepted on: November 18, 2022

Submitted on: January 13, 2022

Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Computer Science and Game Theory,68N30,I.6.4

Licence: Attribution 4.0 International (CC BY 4.0)

Funding:

Source : OpenAIRE Graph

Subgroups of tree almost automorphism groups; Funder: Swiss National Science Foundation; Code: 175106
Cyber Security Network of Competence Centres for Europe; Funder: European Commission; Code: 830929

Classifications

Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

16 Documents citing this article

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Massimo Bartoletti;James Hsin-yu Chiang;Alberto Lluch Lafuente, Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU), Towards a Theory of Decentralized Finance, pp. 227-232, 2021, 10.1007/978-3-662-63958-0_20, https://orbit.dtu.dk/en/publications/8864a294-fee1-4043-97bf-4dd37d3e3d52.

Massimo Bartoletti;James Hsin-yu Chiang;Alberto Lluch-Lafuente, Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU), A Theory of Automated Market Makers in DeFi, pp. 168-187, 2021, 10.1007/978-3-030-78142-2_11, https://backend.orbit.dtu.dk/ws/files/299969633/10709_PDF_file_42900_2_10_20221129.pdf.

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