Batch Exchanges Moo-ving Forward: A Formalization and Empirical Analysis of CowSwap and Other CFMM-Based Clearing Price Auctions

Abstract

One of the most popular cryptocurrency batch exchanges is CowSwap, a constant-function-market-maker-based (CFMM) batch exchange protocol that finds the optimal set of trades within a batch by enlisting other users to solve a complex optimization problem [1]. This complex optimization protocol shares many common attributes with another batch auction problem with uniform clearing prices proposed in March 2021 by Tom Walther [18]. There are, however, significant structural differences between the two, both in the objective of the optimization problem as well as its constraints. However, despite the many versions of such cryptocurrency batch auctions, there is little literature formally constructing the problems, and there is virtually no existing research on how we can expect these batch auctions to behave in various market environments. This paper dissects each of CowSwap’s constraints and leverages this to formalize both Walther’s 2021 problem as well as a minimal version of the CowSwap problem that captures many of its key aspects in Big-M formulation. We then implement these formalizations in Python using the Gurobi solver package and simulate a variety of market conditions in order to better understand the behavior of Walther’s 2021 model as well as CowSwap. Our empirical results indicate that CowSwap is a more stable model that is more capable at extracting utility for the batch when arbitrage opportunities are present in the market. Additionally, we conclude that neither model favors large order sizes over smaller ones, and propose future research regarding what premium a trader should expect to pay to have a large order fulfilled.