Shannon meets Myerson: Information Extraction from a Strategic Sender

TL;DR

This paper introduces a framework for information extraction from a strategic sender using questionnaires, defining a capacity measure that generalizes Shannon capacity to strategic communication scenarios.

Contribution

It develops a new capacity measure for strategic communication, providing bounds and exact evaluations, and advances understanding of noncooperative information exchange.

Findings

The receiver can recover exponentially many sequences despite strategic sender and noise.

Exponential unrecoverability exists, limiting information extraction.

The capacity measure generalizes Shannon capacity for strategic settings.

Abstract

We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, noncooperative regime of communication involving a strategic sender.