Privacy signaling games with binary alphabets

TL;DR

This paper analyzes privacy signaling games with binary messages, exploring equilibrium conditions and strategies for transmitter and receiver interactions under privacy constraints, supported by theoretical derivations and simulations.

Contribution

It introduces a framework for privacy signaling games with binary alphabets, deriving equilibrium conditions and revealing that Nash and Stackelberg equilibria can share strategies.

Findings

Equilibrium conditions depend on mutual information and Hamming distance.

Nash and Stackelberg equilibria can coincide with identical strategies.

Simulation results validate theoretical predictions.

Abstract

In this paper, we consider a privacy signaling game problem for binary alphabets and single-bit transmission where a transmitter has a pair of messages, one of which is a casual message that needs to be conveyed, whereas the other message contains sensitive data and needs to be protected. The receiver wishes to estimate both messages to acquire as much information as possible. For this setup, we study the interactions between the transmitter and the receiver with non-aligned information-theoretic objectives (modeled by mutual information and hamming distance) due to the privacy concerns of the transmitter. We derive conditions under which Nash and/or Stackelberg equilibria exist and identify the optimal responses of the encoder and decoders strategies for each type of game. One particularly surprising result is that when both types of equilibria exist, they admit the same encoding and decoding strategies. We corroborate our analysis with simulation studies.