A Theory of Automated Market Makers in DeFi

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

doi:10.1007/978-3-030-78142-2_11

A Theory of Automated Market Makers in DeFi

Massimo Bartoletti, James Hsin yu Chiang^*, Alberto Lluch-Lafuente

^*Corresponding author for this work

Department of Applied Mathematics and Computer Science

University of Cagliari

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Abstract

Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. They allow users to exchange units of different types of crypto-assets, 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.

Original language	English
Title of host publication	Coordination Models and Languages
Editors	Ferruccio Damiani, Ornela Dardha
Publisher	Springer
Publication date	2021
Pages	168-187
ISBN (Print)	9783030781415
DOIs	https://doi.org/10.1007/978-3-030-78142-2_11
Publication status	Published - 2021
Event	23^rd IFIP WG 6.1 International Conference on Coordination Models and Languagesec 2021 - Virtual, Online Duration: 14 Jun 2021 → 18 Jun 2021 http://www.discotec.org/2021/coordination.html

Conference

Conference	23^rd IFIP WG 6.1 International Conference on Coordination Models and Languagesec 2021
City	Virtual, Online
Period	14/06/2021 → 18/06/2021
Internet address	http://www.discotec.org/2021/coordination.html

Series	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12717 LNCS
ISSN	0302-9743

Bibliographical note

Funding Information:
Massimo Bartoletti is partially supported by Conv. Fondazione di Sardegna & Atenei Sardi project F74I19000900007 ADAM. James Hsin-yu Chiang is supported by the PhD School of DTU Compute. Alberto Lluch Lafuente is partially supported by the EU H2020-SU-ICT-03-2018 Project No. 830929 CyberSec4Europe (cybersec4europe.eu).

Funding Information:
Acknowledgements. Massimo Bartoletti is partially supported by Conv. Fondazione

Publisher Copyright:
© 2021, IFIP International Federation for Information Processing.

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10.1007/978-3-030-78142-2_11

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Bartoletti, M., Chiang, J. H. Y., & Lluch-Lafuente, A. (2021). A Theory of Automated Market Makers in DeFi. In F. Damiani, & O. Dardha (Eds.), Coordination Models and Languages (pp. 168-187). Springer. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Vol. 12717 LNCS https://doi.org/10.1007/978-3-030-78142-2_11

Bartoletti, Massimo ; Chiang, James Hsin yu ; Lluch-Lafuente, Alberto. / A Theory of Automated Market Makers in DeFi. Coordination Models and Languages. editor / Ferruccio Damiani ; Ornela Dardha. Springer, 2021. pp. 168-187 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 12717 LNCS).

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Bartoletti, M, Chiang, JHY & Lluch-Lafuente, A 2021, A Theory of Automated Market Makers in DeFi. in F Damiani & O Dardha (eds), Coordination Models and Languages. Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12717 LNCS, pp. 168-187, 23^rd IFIP WG 6.1 International Conference on Coordination Models and Languagesec 2021, Virtual, Online, 14/06/2021. https://doi.org/10.1007/978-3-030-78142-2_11

A Theory of Automated Market Makers in DeFi. / Bartoletti, Massimo; Chiang, James Hsin yu ; Lluch-Lafuente, Alberto.

Coordination Models and Languages. ed. / Ferruccio Damiani; Ornela Dardha. Springer, 2021. p. 168-187 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 12717 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - A Theory of Automated Market Makers in DeFi

AU - Bartoletti, Massimo

AU - Chiang, James Hsin yu

AU - Lluch-Lafuente, Alberto

N1 - Funding Information: Massimo Bartoletti is partially supported by Conv. Fondazione di Sardegna & Atenei Sardi project F74I19000900007 ADAM. James Hsin-yu Chiang is supported by the PhD School of DTU Compute. Alberto Lluch Lafuente is partially supported by the EU H2020-SU-ICT-03-2018 Project No. 830929 CyberSec4Europe (cybersec4europe.eu). Funding Information: Acknowledgements. Massimo Bartoletti is partially supported by Conv. Fondazione Publisher Copyright: © 2021, IFIP International Federation for Information Processing.

PY - 2021

Y1 - 2021

N2 - Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. They allow users to exchange units of different types of crypto-assets, 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.

AB - Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. They allow users to exchange units of different types of crypto-assets, 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.

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DO - 10.1007/978-3-030-78142-2_11

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Coordination Models and Languages

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Bartoletti M, Chiang JHY , Lluch-Lafuente A. A Theory of Automated Market Makers in DeFi. In Damiani F, Dardha O, editors, Coordination Models and Languages. Springer. 2021. p. 168-187. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 12717 LNCS). doi: 10.1007/978-3-030-78142-2_11

A Theory of Automated Market Makers in DeFi

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