A General Theory of Liquidity Provisioning for Prediction Markets

Liquidity provisioning in automated market makers is the practice of recruiting third-party liquidity providers (LPs) to contribute assets to the market in exchange for fees skimmed off of trades. This paper introduces a general framework for liquidity provisioning in cost function prediction markets. Our most general protocol allows LPs to submit or update an arbitrary cost function that specifies their liquidity over the entire price space. We show that our protocol encapsulates several notions of running market makers in parallel, which we prove to be equivalent. We also recover existing protocols from decentralized finance as special cases. In our protocol, liquidity can be expressed as a matrix-valued function, which we argue is necessary with three or more securities. Due to this inherent multidimensionality, the design of trading fees with three or more securities is nontrivial: we show that natural axioms on the design of these fees are incompatible.