Evolutionary Poisson Games for Controlling Large Population Behaviors

TL;DR

This paper introduces an evolutionary Poisson game framework to model and control large, heterogeneous populations in complex networks, with applications demonstrated in cybersecurity for antivirus adoption.

Contribution

It develops a novel evolutionary Poisson game model, establishes equilibrium properties, and designs convergent online algorithms for system-wide behavior control.

Findings

Existence and uniqueness of evolutionary Poisson stable equilibrium.

Convergence of online algorithms to optimal control solutions.

Numerical validation of the proposed framework and algorithms.

Abstract

Emerging applications in engineering such as crowd-sourcing and (mis)information propagation involve a large population of heterogeneous users or agents in a complex network who strategically make dynamic decisions. In this work, we establish an evolutionary Poisson game framework to capture the random, dynamic and heterogeneous interactions of agents in a holistic fashion, and design mechanisms to control their behaviors to achieve a system-wide objective. We use the antivirus protection challenge in cyber security to motivate the framework, where each user in the network can choose whether or not to adopt the software. We introduce the notion of evolutionary Poisson stable equilibrium for the game, and show its existence and uniqueness. Online algorithms are developed using the techniques of stochastic approximation coupled with the population dynamics, and they are shown to converge to the optimal solution of the controller problem. Numerical examples are used to illustrate and corroborate our results.