Geodesic
Handling a Kullback-Leibler divergence random walk for scheduling effective patrol strategies in Stackelberg security games
Kybernetika, Tome 55 (2019) no. 4, pp. 618-640.

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This paper presents a new model for computing optimal randomized security policies in non-cooperative Stackelberg Security Games (SSGs) for multiple players. Our framework rests upon the extraproximal method and its extension to Markov chains, within which we explicitly compute the unique Stackelberg/Nash equilibrium of the game by employing the Lagrange method and introducing the Tikhonov regularization method. We also consider a game-theory realization of the problem that involves defenders and attackers performing a discrete-time random walk over a finite state space. Following the Kullback-Leibler divergence the players' actions are fixed and, then the next-state distribution is computed. The player's goal at each time step is to specify the probability distribution for the next state. We present an explicit construction of a computationally efficient strategy under mild defenders and attackers conditions and demonstrate the performance of the proposed method on a simulated target tracking problem.
DOI : 10.14736/kyb-2019-4-0618
Classification : 91A10, 91A35, 91A80, 91B06, 91B70, 91B74
Keywords: Stackelberg games; security; patrolling; Markov chains 
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     title = {Handling a {Kullback-Leibler} divergence random walk for scheduling effective patrol strategies in {Stackelberg} security games},
     journal = {Kybernetika},
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Solis, César U. S.; Clempner, Julio B.; Poznyak, Alexander S. Handling a Kullback-Leibler divergence random walk for scheduling effective patrol strategies in Stackelberg security games. Kybernetika, Tome 55 (2019) no. 4, pp. 618-640. doi : 10.14736/kyb-2019-4-0618. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-4-0618/

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