Differential Privacy in Constant Function Market Makers

Chitra, Tarun; Angeris, Guillermo; Evans, Alex

doi:10.1007/978-3-031-18283-9_8

Cited by 3 publications

(1 citation statement)

References 30 publications

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“…Though the idea of a batched exchange has been proposed many times in different contexts (see, e.g., [4] and [13]), presently, almost all major decentralized exchanges are not batched. Recent work has suggested that batching is useful for privacy [5] and Penumbra [9] has proposed a design for a fully-private decentralized exchange which makes use of batching as a method for avoiding certain information leakage [2]. We describe a very simplified version of this proposal below, which will suffice for our discussion.…”

Section: Batched Decentralized Exchangesmentioning

confidence: 99%

Concave Pro-rata Games

Johnson¹,

Diamandis²,

Evans³

et al. 2023

Preprint

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In this paper, we introduce a family of games called concave pro-rata games. In such a game, players place their assets into a pool, and the pool pays out some concave function of all assets placed into it. Each player then receives a pro-rata share of the payout; i.e., each player receives an amount proportional to how much they placed in the pool. Such games appear in a number of practical scenarios, including as a simplified version of batched decentralized exchanges, such as those proposed by Penumbra. We show that this game has a number of interesting properties, including a symmetric pure equilibrium that is the unique equilibrium of this game, and we prove that its price of anarchy is Ω(n) in the number of players. We also show some numerical results in the iterated setting which suggest that players quickly converge to an equilibrium in iterated play.

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