TY - GEN
T1 - Secure Discrete-Time Linear-Quadratic Mean-Field Games
AU - uz Zaman, Muhammad Aneeq
AU - Bhatt, Sujay
AU - Başar, Tamer
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85098258376&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85098258376&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-64793-3_11
DO - 10.1007/978-3-030-64793-3_11
M3 - Conference contribution
AN - SCOPUS:85098258376
SN - 9783030647926
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 203
EP - 222
BT - Decision and Game Theory for Security - 11th International Conference, GameSec 2020, Proceedings
A2 - Zhu, Quanyan
A2 - Baras, John S.
A2 - Poovendran, Radha
A2 - Chen, Juntao
PB - Springer
T2 - 11th Conference on Decision and Game Theory for Security, GameSec 2020
Y2 - 28 October 2020 through 30 October 2020
ER -