Concave Pro-rata Games: Batched decentralized exchanges

Table of Links

Abstract and Introduction

1 The concave pro-rata game

1.1 Symmetric pure strict equilibrium

1.2 Uniqueness of equilibrium

1.3 Equilibrium payoff

2 Batched decentralized exchanges

2.1 Arbitrage

3 Conclusion and References

A Numerics

B Additional Numerics

C Relaxing strict concavity

D Rosen condition

2 Batched decentralized exchanges

In this section, we will show some basic applications of the above properties to a batched decentralized exchange, which we describe below.

Decentralized exchanges. A decentralized exchange (or DEX, for short) is a type of exchange that exists on a blockchain. Such exchanges enable any agent to trade currencies without the need for a centralized intermediary. In many cases, these exchanges are organized as constant function market makers (see, e.g., [1] for a general introduction to this type of exchange), a special type of automated market maker that uses a specific function to price assets.

Batched DEXs. A batched decentralized exchange is a DEX where the trades are batched before they are executed. Specifically, the trades are aggregated in some way (depending on the type of batching performed) and then traded ‘all together’ through the DEX, before being disaggregated and passed back to the users. 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.