Fictitious play with time-invariant frequency update for network security

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 ..