Online Mechanism Design for Information Acquisition

TL;DR

This paper develops algorithms for online incentive-compatible mechanisms in information acquisition, balancing truthful reporting and utility maximization in sequential, uncertain interactions.

Contribution

It introduces efficient algorithms for computing optimal incentive-compatible mechanisms and extends to online settings with regret and violation guarantees.

Findings

Full feedback algorithm achieves ( ilde{ ext{O}}(\u2212rac{1}{2}T)) regret and violation.

Bandit feedback algorithm attains ( ilde{ ext{O}}(T^{ ext{alpha}})) regret and ( ilde{ ext{O}}(T^{1- ext{alpha}/2})) violation.

Provides a tight lower bound for the online information acquisition problem.

Abstract

We study the problem of designing mechanisms for \emph{information acquisition} scenarios. This setting models strategic interactions between an uniformed \emph{receiver} and a set of informed \emph{senders}. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal \emph{incentive compatible} (IC) mechanism. Then, we focus on the \emph{online} problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the \emph{cumulative regret} w.r.t. the optimal IC mechanism, and the \emph{cumulative violation} of the incentive compatibility constraints. We investigate two different online scenarios, \emph{i.e.,} the \emph{full} and \emph{bandit feedback} settings. For the full feedback problem, we propose an algorithm that guarantees $\tilde{\mathcal O}(\sqrt T)$ regret and violation, while for the bandit feedback setting we present an algorithm that attains $\tilde{\mathcal O}(T^{\alpha})$ regret and $\tilde{\mathcal O}(T^{1-\alpha/2})$ violation for any $\alpha\in[1/2, 1]$. Finally, we complement our results providing a tight lower bound.