Fictitious play with time-invariant frequency update for network security

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.

[1]  Ulrich Berger Fictitious play in 2xn games , 2003 .

[2]  Tansu Alpcan,et al.  Security Games with Incomplete Information , 2009, 2009 IEEE International Conference on Communications.

[3]  T. Basar,et al.  A game theoretic analysis of intrusion detection in access control systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[4]  Tansu Alpcan,et al.  Security games with decision and observation errors , 2010, Proceedings of the 2010 American Control Conference.

[5]  T. Basar,et al.  A game theoretic approach to decision and analysis in network intrusion detection , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[6]  Jeff S. Shamma,et al.  Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria , 2005, IEEE Transactions on Automatic Control.

[7]  Lin Chen,et al.  On Selfish and Malicious Behaviors in Wireless Networks - a Non-cooperative Game Theoretic Approach. (Sur les Comportements Égoïstes et Malveillants dans les Réseaux sans Fil - une Approche base sur la Théorie des Jeux Non-coopératifs) , 2008 .

[8]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[9]  Shie Mannor,et al.  Online calibrated forecasts: Memory efficiency versus universality for learning in games , 2006, Machine Learning.

[10]  Karin Sallhammar,et al.  Stochastic Models for Combined Security and Dependability Evaluation , 2007 .

[11]  Jeff S. Shamma,et al.  Unified convergence proofs of continuous-time fictitious play , 2004, IEEE Transactions on Automatic Control.

[12]  J. Robinson AN ITERATIVE METHOD OF SOLVING A GAME , 1951, Classics in Game Theory.

[13]  Jean-Pierre Hubaux,et al.  Security and Cooperation in Wireless Networks , 2007, ESAS.

[14]  T. Başar,et al.  An Intrusion Detection Game with Limited Observations , 2005 .

[15]  Gerald Keller,et al.  Statistics for Management and Economics , 1990 .

[16]  Chase Qishi Wu,et al.  A Survey of Game Theory as Applied to Network Security , 2010, 2010 43rd Hawaii International Conference on System Sciences.

[17]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[18]  Tansu Alpcan,et al.  Stochastic games for security in networks with interdependent nodes , 2009, 2009 International Conference on Game Theory for Networks.