A Theory of Automated Market Makers in DeFi

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

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

Cited by 22 publications

(9 citation statements)

References 11 publications

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“…Comparison with previous work. A preliminary version of this work was presented at COORDINATION 2021 [BCL21b]. The current version substantially extends it, streamlining the theory and providing additional results.…”

Section: Introductionmentioning

confidence: 82%

“…The current version substantially extends it, streamlining the theory and providing additional results. A crucial difference between the two papers is that, while in [BCL21b] the semantics of swap actions was parameterized by an invariant between the old and the new token reserves, here we make the semantics parametric w.r.t. the swap rate function SX .…”

Section: Introductionmentioning

confidence: 99%

“…Among the new results w.r.t. [BCL21b], we mention in particular the additivity and reversibility properties (Theorems 4.10,4.11,5.6,and 5.9), and the results that relate the gain of swaps before and after deposit/redeem actions (Theorems 6.6, 6.9, 6.8, and 6.10). Besides these extensions, the current paper includes a discussion of the constant sum and of the constant mean swap rate functions, a new section on MEV attacks (see section 7), and it provides detailed proofs for all its statements.…”

Section: Introductionmentioning

confidence: 99%

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A theory of Automated Market Makers in DeFi

Bartoletti¹,

Chiang²,

Lafuente³

2022

Logical Methods in Computer Science

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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.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A theory of Automated Market Makers in DeFi

Bartoletti¹,

Chiang²,

Lafuente³

2022

Logical Methods in Computer Science

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“…Alternatively, trading against multiple AMMs was presented within [15]. [9] provides a generalized structure for the interactions that can occur between investors and the AMM. We refer the interested reader to [20] for a summary of terminology and structures that are currently used in practice in this field.…”

Section: Literature Reviewmentioning

confidence: 99%

Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance

Bichuch¹,

Feinstein²

2022

Preprint

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Within this work we consider an axiomatic framework for Automated Market Makers (AMMs).By imposing reasonable axioms on the underlying utility function, we are able to characterize the properties of the swap size of the assets and of the resulting pricing oracle. We have analyzed many existing AMMs and shown that the vast majority of them satisfy our axioms. We have also considered the question of fees and divergence loss. In doing so, we have proposed a new fee structure so as to make the AMM indifferent to transaction splitting. Finally, we have proposed a novel AMM that has nice analytical properties and provides a large range over which there is no divergence loss.

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“…In particular, there are few studies on decentralized crypto exchanges, primarily from practitioners and the Computer Science community. Angeris et al (2021) shows that the AMM can track the market price closely under no-arbitrage conditions; Bartoletti, Chiang, and Lluch-Lafuente (2021) abstracts the AMM away from the actual underlying economic mechanisms and studies its mathematical properties; Daian et al (2020) provides empirical evidence for the existence of arbitrage at AMM. Harvey, Ramachandran, and Santoro (2021) provides a good survey of the DeFi applications.…”

Section: Introductionmentioning

confidence: 99%