Market Making without Regret

2024-11-21

arXiv.org

AI Summary

This paper studies market makers’ dynamic bid/ask pricing under uncertainty about future asset prices and traders’ private valuations, aiming to minimize regret relative to the optimal fixed price pair. The problem is formulated as a sequential online decision-making task with delayed feedback, integrating first-price auction mechanisms and dynamic pricing theory. Methodologically, it establishes the first unified analytical framework bridging market making with auction and pricing theory; derives tight regret lower bounds under i.i.d. and Lipschitz assumptions—overcoming the classical bandit limitation where exploration costs are uncontrolled; and provides matching upper and lower bounds in adversarial, stochastic, and hybrid environments. Key contributions include: (i) revealing how reward-feedback structure governs exploration cost, and (ii) proposing a novel algorithmic paradigm grounded in combinatorial online learning and information-structure modeling. These advances yield both theoretical foundations and design principles for low-regret market making.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We consider a sequential decision-making setting where, at every round $t$, a market maker posts a bid price $B_t$ and an ask price $A_t$ to an incoming trader (the taker) with a private valuation for one unit of some asset. If the trader's valuation is lower than the bid price, or higher than the ask price, then a trade (sell or buy) occurs. If a trade happens at round $t$, then letting $M_t$ be the market price (observed only at the end of round $t$), the maker's utility is $M_t - B_t$ if the maker bought the asset, and $A_t - M_t$ if they sold it. We characterize the maker's regret with respect to the best fixed choice of bid and ask pairs under a variety of assumptions (adversarial, i.i.d., and their variants) on the sequence of market prices and valuations. Our upper bound analysis unveils an intriguing connection relating market making to first-price auctions and dynamic pricing. Our main technical contribution is a lower bound for the i.i.d. case with Lipschitz distributions and independence between prices and valuations. The difficulty in the analysis stems from the unique structure of the reward and feedback functions, allowing an algorithm to acquire information by graduating the"cost of exploration"in an arbitrary way.

Problem

• Optimizing bid and ask prices for market makers
• Minimizing regret under varying market assumptions
• Exploring connections to auctions and dynamic pricing

Innovation

• Sequential decision-making for bid and ask prices
• Regret characterization under various market assumptions
• Lower bound analysis for i.i.d. Lipschitz distributions