DeFi

Optimal Automated Market Makers: Differentiable Economics and Strong Duality ArXiv ID: 2402.09129 “View on arXiv” Authors: Unknown Abstract The role of a market maker is to simultaneously offer to buy and sell quantities of goods, often a financial asset such as a share, at specified prices. An automated market maker (AMM) is a mechanism that offers to trade according to some predetermined schedule; the best choice of this schedule depends on the market maker’s goals. The literature on the design of AMMs has mainly focused on prediction markets with the goal of information elicitation. More recent work motivated by DeFi has focused instead on the goal of profit maximization, but considering only a single type of good (traded with a numeraire), including under adverse selection (Milionis et al. 2022). Optimal market making in the presence of multiple goods, including the possibility of complex bundling behavior, is not well understood. In this paper, we show that finding an optimal market maker is dual to an optimal transport problem, with specific geometric constraints on the transport plan in the dual. We show that optimal mechanisms for multiple goods and under adverse selection can take advantage of bundling, both improved prices for bundled purchases and sales as well as sometimes accepting payment “in kind.” We present conjectures of optimal mechanisms in additional settings which show further complex behavior. From a methodological perspective, we make essential use of the tools of differentiable economics to generate conjectures of optimal mechanisms, and give a proof-of-concept for the use of such tools in guiding theoretical investigations. ...

All AMMs are CFMMs. All DeFi markets have invariants. A DeFi market is arbitrage-free if and only if it has an increasing invariant ArXiv ID: 2310.09782 “View on arXiv” Authors: Unknown Abstract In a universal framework that expresses any market system in terms of state transition rules, we prove that every DeFi market system has an invariant function and is thus by definition a CFMM; indeed, all automated market makers (AMMs) are CFMMs. Invariants connect directly to arbitrage and to completeness, according to two fundamental equivalences. First, a DeFi market system is, we prove, arbitrage-free if and only if it has a strictly increasing invariant, where arbitrage-free means that no state can be transformed into a dominated state by any sequence of transactions. Second, the invariant is, we prove, unique if and only if the market system is complete, meaning that it allows transitions between all pairs of states in the state space, in at least one direction. Thus a necessary and sufficient condition for no-arbitrage (respectively, for completeness) is the existence of the increasing (respectively, the uniqueness of the) invariant, which, therefore, fulfills in nonlinear DeFi theory the foundational role parallel to the existence (respectively, uniqueness) of the pricing measure in the Fundamental Theorem of Asset Pricing for linear markets. Moreover, a market system is recoverable by its invariant if and only if it is complete; and in all cases, complete or incomplete, every market system has, and is recoverable by, a multi-invariant. A market system is arbitrage-free if and only if its multi-invariant is increasing. Our examples illustrate (non)existence of various specific types of arbitrage in the context of various specific types of market systems – with or without fees, with or without liquidity operations, and with or without coordination among multiple pools – but the fundamental theorems have full generality, applicable to any DeFi market system and to any notion of arbitrage expressible as a strict partial order. ...