Achievable Rates for Information Extraction from a Strategic Sender

TL;DR

This work introduces a novel information-theoretic framework for information extraction from a strategic sender, modeling the interaction as a Stackelberg game with the receiver as the leader. It establishes a rate-based characterization of reliable recovery under distortion, identifying a sufficient (and in the binary lossless case, necessary) condition on the sender’s utility that enables a nonempty rate region. A key finding is the existence of a maximum achievable rate, generally below the channel capacity, arising from incentives that allow the sender to misreport information; the receiver mitigates this by selective decoding that recovers a subset of high-probability sequences. The analysis covers both binary and general alphabets, with lossy and lossless recovery results, and provides illustrative examples demonstrating rate gaps and the role of type-class structure in constraining information leakage.

Abstract

We consider a setting of non-cooperative communication where a receiver wants to recover randomly generated sequences of symbols that are observed by a strategic sender. The sender aims to maximize an average utility that may not align with the recovery criterion of the receiver, whereby the signals it sends may not be truthful. The rate of communication is defined as the number of reconstructions corresponding to the sequences recovered correctly while communicating with the sender. We pose this problem as a sequential game between the sender and the receiver with the receiver as the leader and determine strategies for the receiver that attain vanishing probability of error and compute the rates of such strategies. We show the existence of such strategies under a condition on the utility of the sender. For the case of the binary alphabet, this condition is also necessary, in the absence of which, the probability of error goes to one for all choices of strategies of the receiver. We show that for reliable recovery, the receiver chooses to correctly decode only a $\textit{subset}$ of messages received from the sender and deliberately makes an error on messages outside this subset. Despite a clean channel, our setting exhibits a non-trivial $\textit{maximum}$ rate of communication, which is in general strictly less than the capacity of the channel. This implies the impossibility of strategies that correctly decode sequences of rate greater than the maximum rate while also achieving reliable communication. This is a key point of departure from the usual setting of cooperative communication.

Figures (3)

• Figure 1: Communication setup between the strategic sender and the receiver
• Figure 2: Rate region (lossless recovery, binary alphabet) : a) the rate region is empty whenever $\mathscr{U}(0,1)+ \mathscr{U}(1,0) \geq 0$, b) for $\mathscr{U}(0,1)+ \mathscr{U}(1,0) < 0$, $\mathscr{U}(0,1)\mathscr{U}(1,0)\leq 0$, the rate region is $\tilde{{\cal R}} \subseteq [H(p), R] , R \leq H(\min\{bp/a,1/2\})$, c) the rate region is same as Shannon rate region for $\mathscr{U}(0,1),\mathscr{U}(1,0) < 0$
• Figure 3: Comparison of ${\mathbb{P}}({\cal D}_\delta(g_n^i,s_n^i))$ for some $s_n^i \in \mathscr{B}(g_n^i)$ with the cooperative setting

Theorems & Definitions (69)

• Definition 2.1: Best response strategy set
• Theorem 2.1
• proof
• Definition 2.2: Rate of communication
• Definition 2.3: Achievable rate
• Theorem 2.2: Convexity of rate region
• proof
• Theorem 3.1: Lossless rate region
• proof
• Theorem 3.2: Lossy rate region