We introduce a setting where a receiver aims to perfectly recover a source known privately to a \textit{strategic} sender over a possibly noisy channel. The sender is endowed with a utility function and sends signals to the receiver with the aim of maximizing this utility. Due to the strategic nature of the sender not all the transmitted information is truthful, which leads to question: how much true information can be recovered by the receiver from such a sender? We study this question in this paper. We pose the problem as a game between the sender and receiver, where the receiver tries to maximize the number of sequences that can be recovered perfectly and the sender maximizes its utility. We show that, in spite of the sender being strategic and the presence of noise in the channel, there is a strategy for the receiver by which it can perfectly recover an \textit{exponentially} large number of sequences. Our analysis leads to the notion of the \textit{information extraction capacity} of the sender which quantifies the growth rate of the number of recovered sequences with blocklength, in the presence of a noiseless channel. We identify cases where this capacity is equal to its theoretical maximum, and also when it is strictly less than maximum. In the latter case, we show that the capacity is sandwiched between the independence number and the Shannon capacity of a suitably defined graph. These results lead to an exact characterization of the information extraction capacity in large number of cases. We show that in the presence of a noisy channel, the rate of information extraction achieved by the receiver is the minimum of the zero-error capacity of the channel and the information extraction capacity of the sender. Our analysis leads to insights into a novel regime of communication involving strategic agents.

中文翻译：

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从战略发送者那里提取信息：零错误案例

我们引入了一种设置，其中接收者旨在通过可能有噪声的通道完美地恢复 \textit{strategic} 发送者私下知道的源。发送方具有效用函数，并向接收方发送信号，目的是使效用最大化。由于发送者的战略性质，并非所有传输的信息都是真实的，这就引出了一个问题：接收者可以从这样的发送者那里恢复多少真实信息？我们在本文中研究了这个问题。我们将问题视为发送方和接收方之间的博弈，其中接收方尝试最大化可以完美恢复的序列数量，而发送方最大化其效用。我们表明，尽管发送方具有策略性并且信道中存在噪声，接收器有一种策略，通过它可以完美地恢复 \textit{exponentially} 大量序列。我们的分析导致了发送方的 \textit{信息提取能力} 的概念，该概念量化了在无噪声信道存在的情况下具有块长度的恢复序列数量的增长率。我们确定此容量等于其理论最大值的情况，以及严格小于最大值的情况。在后一种情况下，我们表明容量夹在适当定义的图的独立数和香农容量之间。这些结果导致在大量情况下准确表征信息提取能力。我们表明，在存在噪声信道的情况下，接收端达到的信息抽取率是信道的零差错容量和发送端的信息抽取能力中的最小值。我们的分析导致对涉及战略代理人的新型沟通机制的深入了解。