[论文解读] Information Extraction from a Strategic Sender: The Zero Error Case.

Anuj S. Vora, Ankur A. Kulkarni|arXiv (Cornell University)|Jun 18, 2020

Game Theory and Applications参考文献 26被引用 5

一句话总结

本文研究了在噪声信道中，来自策略性发送方的信息提取问题，其中发送方通过扭曲信号以最大化自身效用。尽管存在策略性歪曲和噪声干扰，接收方仍能通过利用博弈论策略，完美恢复指数级数量的源序列，实现依赖于发送方效用结构和信道特性的零错误信息提取容量。

ABSTRACT

We introduce a setting where a receiver aims to perfectly recover a source known privately to a extit{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 extit{exponentially} large number of sequences. Our analysis leads to the notion of the extit{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.

研究动机与目标

• 理解当与策略性发送方通信时，接收方能够完美恢复的忠实信息量有多大，该发送方会扭曲信号以最大化自身效用。
• 将发送方与接收方的互动建模为一个博弈，其中接收方旨在最大化可恢复序列数量，而发送方旨在通过策略性信号传输最大化效用。
• 定义并刻画在策略性信号传输下，信息提取容量——即与块长相关的可恢复序列数的指数增长率——的特性。
• 确定该容量何时达到理论最大值，何时严格小于最大值，并通过图论工具识别结构性约束。
• 通过证明可达率是信道零错误容量与发送方信息提取容量的最小值，将分析扩展至噪声信道。

提出的方法

• 将发送方-接收方互动建模为一个双人博弈，双方目标相反：接收方最大化可恢复序列数，发送方通过策略性信号传输最大化效用。
• 将信息提取容量定义为在无噪声信道下，完美可恢复序列数的指数增长率，其参数由发送方的效用函数决定。
• 使用图论构造：通过适当定义的图表示发送方的信号约束，利用独立数和香农容量对信息提取容量提供上下界。
• 证明信息提取容量被限定在所定义图的独立数与香农容量之间，从而在许多情况下实现精确刻画。
• 通过结合信道的零错误容量与发送方的信息提取容量，分析噪声信道情形，证明整体速率是两者的最小值。
• 应用博弈论均衡分析，推导出即使在策略性发送方行为和信道噪声下也能确保完美恢复的接收方策略。

实验结果

研究问题

• RQ1 当发送方具有策略性且可能扭曲信息时，接收方最多能完美恢复多少个源序列？
• RQ2 发送方效用函数的结构如何影响信息提取的可达速率？
• RQ3 在什么情况下信息提取容量等于其理论最大值，而在什么情况下严格小于最大值？
• RQ4 如何利用图论概念（如独立数和香农容量）来刻画信息提取容量？
• RQ5 当通信信道存在噪声时，信息提取的根本极限是什么？

主要发现

• 即使发送方具有策略性且信道存在噪声，接收方仍能实现对指数级数量源序列的完美恢复。
• 信息提取容量被限定在由发送方信号约束所导出图的独立数与香农容量之间。
• 在许多情况下，信息提取容量可被精确刻画，尤其当图结构允许紧密边界时。
• 当信道存在噪声时，信息提取的可达速率是信道零错误容量与发送方信息提取容量的最小值。
• 当发送方效用函数与真实传输对齐时，容量达到最大；当策略激励导致扭曲时，容量降低。
• 该框架揭示了一种涉及策略性参与者的新型通信模式，在此模式下，尽管存在误导动机，仍可实现完美恢复。