Market Making without Regret

Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Luigi Foscari, Vinayak Pathak

Keywords: Regret minimization, online learning, market making, first-price auctions, dynamic pricing

TL;DR: We characterize the regret of a market maker 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.

Abstract:

We consider a sequential decision-making setting where, at every round $t$, the learner (a \emph{market maker}) post
s a \emph{bid} price $B_t$ and an \emph{ask} price $A_t$ to an incoming trader (the \emph{taker}) with a private
valuation for 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) occu
rs.
Letting $P_t$ be the market price (observed only at the end of round $t$), the maker's utility is $P_t-B_t$ if
the maker bought the asset, it is $A_t-P_t$ if they sold it, and it is $0$ if no trade occurred.
We characterize the maker's regret with respect to the best fixed choice of bid and ask pairs under a variety of ass
umptions (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 market prices and takers' valuations.
The difficulty in the analysis stems from a unique relationship between the reward and feedback functions that allow
s learning algorithms to trade off reward for information in a continuous way.

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Track: Fast Track: published work

Publication Link: [e-mail]

Submission Number: 12