Fictitious Play with Time-Invariant Frequency Update for Network Security

TL;DR

This paper introduces a novel time-invariant frequency update scheme for fictitious play in two-player security games, analyzing its convergence and stability, and proposing an adaptive algorithm for improved strategic learning.

Contribution

It proposes a new time-invariant frequency update method for fictitious play, with convergence analysis and an adaptive algorithm for security game strategies.

Findings

Proves local stability of equilibrium with two actions.

Establishes convergence properties of the mean dynamic.

Introduces an adaptive algorithm based on the new update scheme.

Abstract

We study two-player security games which can be viewed as sequences of nonzero-sum matrix games played by an Attacker and a Defender. The evolution of the game is based on a stochastic fictitious play process, where players do not have access to each other's payoff matrix. Each has to observe the other's actions up to present and plays the action generated based on the best response to these observations. In a regular fictitious play process, each player makes a maximum likelihood estimate of her opponent's mixed strategy, which results in a time-varying update based on the previous estimate and current action. In this paper, we explore an alternative scheme for frequency update, whose mean dynamic is instead time-invariant. We examine convergence properties of the mean dynamic of the fictitious play process with such an update scheme, and establish local stability of the equilibrium point when both players are restricted to two actions. We also propose an adaptive algorithm based on this time-invariant frequency update.