Market Making without Regret

ArXiv ID: 2411.13993 “View on arXiv”

Authors: Unknown

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.

Keywords: market making, sequential decision-making, regret analysis, bid-ask spread, dynamic pricing, Asset Trading (General)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper presents heavy theoretical analysis with dense mathematical formalism (online learning, regret bounds, Lipschitz distributions, lower bounds), placing it in the ‘Lab Rats’ quadrant due to high math complexity and low empirical rigor.

  flowchart TD
    A["Research Goal"] --> B["Modeling & Setup"]
    B --> C["Regret Analysis"]
    C --> D{"Assumption on<br/>Market & Valuation"}
    D --> E["Adversarial Case"]
    D --> F["I.I.D. Case"]
    E --> G["Regret Bound via<br/>Adversarial Dynamic Pricing"]
    F --> H["Lower Bound Derivation<br/>with Lipschitz Distributions"]
    G --> I["Key Outcomes<br/>Regret Bounds & Connection to<br/>First-Price Auctions / Dynamic Pricing"]
    H --> I