Security games with decision and observation errors

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. 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. However, when the game is played over a communication network, there are several practical issues that need to be taken into account: First, the players may make random decision errors from time to time. Second, the players' observations of each other's previous actions may be incorrect. The players will try to compensate for these errors based on the information they have. We examine convergence property of the game in such scenarios, and establish convergence to the equilibrium point under some mild assumptions when both players are restricted to two actions.

[1]  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).

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

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

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

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

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

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

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

[9]  Cristina Comaniciu,et al.  A Bayesian game approach for intrusion detection in wireless ad hoc networks , 2006, GameNets '06.

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

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

[12]  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).

[13]  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 .

[14]  K. Miyasawa.  ON THE CONVERGENCE OF THE LEARNING PROCESS IN A 2 X 2 NON-ZERO-SUM TWO-PERSON GAME , 1961 .

[15]  Ulrich Berger,et al.  Fictitious play in 2×n games , 2005, J. Econ. Theory.