Learning to Price with Persuasion

Maria-Florina Balcan; Tejas Pagare; Karan Singh

cs.GTAug 17, 2026

Learning to Price with Persuasion

Authors: Maria-Florina Balcan, Tejas Pagare, Karan Singh

Organizations: Carnegie Mellon University, Pittsburgh, USA

Abstract

Motivated by modern marketplaces, where the platform or the seller routinely gathers detailed user profiles, we study a novel learning theoretic model that simultaneously involves information and mechanism design. Specifically, we consider the economic setting recently introduced by Bergemann et al. (2022), where in addition to the menu of quality-price pairs, the seller offers information on the value of the match between product quality and buyer's taste via a signaling scheme. We relax the assumption that the seller knows the buyers' belief about the distribution of tastes and study the sample requirements of designing a revenue maximizing scheme. We consider both the batch setting where we have access to data from a set of i.i.d. buyers and an online demand query model where we observe the buyers' behaviors to seller's schemes. Despite the apparent non-convexity of the problem, we also give the first FPTAS to compute a scheme that maximizes the revenue within an arbitrarily small additive loss, which was left open by Bergemann et al. (2022). Overall, this brings a new learning perspective in asymmetric economic settings where buyers and sellers know different types of information.

Figures & tables

Model	Value distribution	Sample Complexity / Regret
Value samples	Arbitrary	$\widetilde{\mathcal{O}}(1/\varepsilon^{3})$
Demand queries	Discrete	$\mathcal{O}(1)$
	Bounded pdf	$\widetilde{\mathcal{O}}(1/\varepsilon^{2})$
	Lipschitz pdf	$\widetilde{\mathcal{O}}(1/\varepsilon)$
	Analytic pdf	$\mathcal{O}(\textrm{polylog }1/\varepsilon)$
Joint learning	Arbitrary	$\widetilde{\mathcal{O}}(T^{3/4})$

Figure 1: Summary of our results. For value samples and demand queries, we list the sample requirements to produce an

\varepsilon

-optimal menu along with the associated signaling scheme. The last row lists the regret in a

T

-horizon game.

\displaystyle\tilde{\pi}(s\mid v)=\begin{cases}\pi(s\mid v)&\text{ if }s\notin\bm{z}_{\tau},\\ \sum_{k\in\bm{z}_{\tau}}\pi(k\mid v)&\text{ if }s=\texttt{null}\end{cases}

Algorithm 1 Empirical Revenue Maximization

(\mathsf{ERM})

via Samples

\displaystyle\tilde{\pi}(s\mid v)=\begin{cases}\pi_{k}(s\mid v)&\text{ if }s\notin\bm{z}_{\tau},\\ \sum_{k\in\bm{z}_{\tau}}\pi_{k}(k\mid v)&\text{ if }s=\texttt{null}\end{cases}

Algorithm 3 Empirical Revenue Maximization via Demand Queries

Bayesian Persuasion

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Data Market Design through Deep Learning

Sai Srivatsa Ravindranath, Yanchen Jiang, David C. Parkes

Harvard John A. Paulson School of Engineering and Applied Sciences

Mechanism Design Information Design

Open paper AskPDF arXiv

The data market design problem is a problem in economic theory to find a set of signaling schemes (statistical experiments) to maximize expected revenue to the information seller, where each experiment reveals some of the information known to a seller and has a corresponding price [Bergemann et al., 2018]. Each buyer has their own decision to make in a world environment, and their subjective expected value for the information associated with a particular experiment comes from the improvement in this decision and depends on their prior and value for different outcomes. In a setting with multiple buyers, a buyer's expected value for an experiment may also depend on the information sold to others [Bonatti et al., 2022]. We introduce the application of deep learning for the design of revenue-optimal data markets, looking to expand the frontiers of what can be understood and achieved. Relative to earlier work on deep learning for auction design [Dütting et al., 2023], we must learn signaling schemes rather than allocation rules and handle obedience constraints

-

these arising from modeling the downstream actions of buyers

-

in addition to incentive constraints on bids. Our experiments demonstrate that this new deep learning framework can almost precisely replicate all known solutions from theory, expand to more complex settings, and be used to establish the optimality of new designs for data markets and make conjectures in regard to the structure of optimal designs.

Abstract

Bayesian Persuasion

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