Remote Estimation Games with Random Walk Processes: Stackelberg Equilibrium

TL;DR

This paper models remote estimation as a strategic game between attacker and defender, incorporating information leakage and analyzing the Stackelberg Equilibrium to improve understanding of optimal sampling under adversarial conditions.

Contribution

It introduces a game-theoretic framework for remote estimation with information leakage, characterizing the Stackelberg Equilibrium for stationary sampling policies.

Findings

Characterized the Stackelberg Equilibrium in the proposed game.

Demonstrated the effectiveness of the equilibrium strategies through simulations.

Provided insights into strategic sampling under adversarial surveillance.

Abstract

Remote estimation is a crucial element of real time monitoring of a stochastic process. While most of the existing works have concentrated on obtaining optimal sampling strategies, motivated by malicious attacks on cyber-physical systems, we model sensing under surveillance as a game between an attacker and a defender. This introduces strategic elements to conventional remote estimation problems. Additionally, inspired by increasing detection capabilities, we model an element of information leakage for each player. Parameterizing the game in terms of uncertainty on each side, information leakage, and cost of sampling, we consider the Stackelberg Equilibrium (SE) concept where one of the players acts as the leader and the other one as the follower. By focusing our attention on stationary probabilistic sampling policies, we characterize the SE of this game and provide simulations to show the efficacy of our results.