Corruption and botnet defense: a mean field game approach

TL;DR

This paper extends mean-field game models for cyber-security issues like corruption and botnet defense to larger state spaces, introducing new asymptotic regimes and establishing a link between stationary and time-dependent solutions.

Contribution

It develops a more general mean-field game model with larger state spaces and introduces novel asymptotic regimes to analyze technical challenges.

Findings

Introduction of small discount and small interaction asymptotics.

Rigorous connection between stationary and time-dependent solutions.

Application of turnpike theory in a mean-field-game context.

Abstract

Recently developed toy models for the mean-field games of corruption and botnet defence in cyber-security with three or four states of agents are extended to a more general mean-field-game model with $2d$ states, $d\in \N$. In order to tackle new technical difficulties arising from a larger state-space we introduce new asymptotic regimes, namely small discount and small interaction asymptotics. Moreover, the link between stationary and time-dependent solutions is established rigorously leading to a performance of the turnpike theory in a mean-field-game setting.