Proofs and Limitations of the Pathway Protocol

Abstract

Blockchain technology offers efficient solutions for a multitude of use-cases, but one of the most successful areas in which this technology has been applied is the field of decentralized finance (DeFi). Decentralized exchanges allow a large number of users to exchange one cryptocurrency for another, without the need for any central authority with any degree of control over the process. Although many different models of decentralized exchanges have been proposed, the Automated Market Maker model currently seems to be the most widely applicable and, therefore, successful. As in the classical financial world, companies and projects may seek to solicit or provide market making services for various trading pairs on exchanges. While for orderbook-based exchanges, the execution of such services is studied deeply and rather straightforward, for AMMs the process becomes more complicated. To solve this, different approaches to market making are offered by the Pathway protocol, focused on two major goals: first, to bring the token price for a particular trading pair to a certain target price, and second, to keep the liquidity of that trading pair intact. The original publication on the Pathway protocol describes its design and goals in detail, but lacks mathematical evidence that the protocol is formally capable of achieving these goals. Therefore, this paper delves a little deeper into the mathematical background of the protocol and formally proves its most important characteristics claimed by the original paper. Last but not least, this paper provides a more in depth discussion of the benefits and limitations of the Pathway protocol, based on the presented mathematical foundations.