Secure Discrete-Time Linear-Quadratic Mean-Field Games

Muhammad Aneeq uz Zaman, Sujay Bhatt, Tamer Başar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we propose a framework for strategic interaction among a large population of agents. The agents are linear stochastic control systems having a communication channel between the sensor and the controller for each agent. The strategic interaction is modeled as a Secure Linear-Quadratic Mean-Field Game (SLQ-MFG), within a consensus framework, where the communication channel is noiseless, but, is susceptible to eavesdropping by adversaries. For the purposes of security, the sensor shares only a sketch of the states using a private key. The controller for each agent has the knowledge of the private key, and has fast access to the sketches of states from the sensor. We propose a secure communication mechanism between the sensor and controller, and a state reconstruction procedure using multi-rate sensor output sampling at the controller. We establish that the state reconstruction is noisy, and hence the Mean-Field Equilibrium (MFE) of the SLQ-MFG does not exist in the class of linear controllers. We introduce the notion of an approximate MFE (ϵ -MFE) and prove that the MFE of the standard (non-secure) LQ-MFG is an ϵ -MFE of the SLQ-MFG. Also, we show that ϵ→ 0 as the estimation error in state reconstruction approaches 0. Furthermore, we show that the MFE of LQ-MFG is also an (ϵ+ ε) -Nash equilibrium for the finite population version of the SLQ-MFG; and (ϵ+ ε) → 0 as the estimation error approaches 0 and the number of agents n→ ∞. We empirically investigate the performance sensitivity of the (ϵ+ ε) -Nash equilibrium to perturbations in sampling rate, model parameters, and private keys.

Original languageEnglish (US)
Title of host publicationDecision and Game Theory for Security - 11th International Conference, GameSec 2020, Proceedings
EditorsQuanyan Zhu, John S. Baras, Radha Poovendran, Juntao Chen
PublisherSpringer Science and Business Media Deutschland GmbH
Pages203-222
Number of pages20
ISBN (Print)9783030647926
DOIs
StatePublished - 2020
Event11th Conference on Decision and Game Theory for Security, GameSec 2020 - College Park, United States
Duration: Oct 28 2020Oct 30 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12513 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th Conference on Decision and Game Theory for Security, GameSec 2020
CountryUnited States
CityCollege Park
Period10/28/2010/30/20

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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