Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games

In a class of games known as Stackelberg games, one agent (the leader) must commit to a strategy that can be observed by the other agent (the follower or adversary) before the adversary chooses its own strategy. We consider Bayesian Stackelberg games, in which the leader is uncertain about the types of adversary it may face. Such games are important in security domains, where, for example, a security agent (leader) must commit to a strategy of patrolling certain areas, and a robber (follower) has a chance to observe this strategy over time before choosing its own strategy of where to attack. This paper presents an efficient exact algorithm for finding the optimal strategy for the leader to commit to in these games. This algorithm, DOBSS, is based on a novel and compact mixed-integer linear programming formulation. Compared to the most efficient algorithm known previously for this problem, DOBSS is not only faster, but also leads to higher quality solutions, and does not suffer from problems of infeasibility that were faced by this previous algorithm. Note that DOBSS is at the heart of the ARMOR system that is currently being tested for security scheduling at the Los Angeles International Airport.

[1]  G. Nemhauser,et al.  Integer Programming , 2020 .

[2]  R. Selten,et al.  A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information , 1972 .

[3]  Bernhard von Stengel,et al.  Fast algorithms for finding randomized strategies in game trees , 1994, STOC '94.

[4]  Ariel Orda,et al.  Achieving network optima using Stackelberg routing strategies , 1997, TNET.

[5]  Avi Pfeffer,et al.  Representations and Solutions for Game-Theoretic Problems , 1997, Artif. Intell..

[6]  Timothy W. McLain,et al.  Multiple UAV cooperative search under collision avoidance and limited range communication constraints , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  Stefan Arnborg,et al.  Bayesian Games for Threat Prediction and Situation Analysis , 2004 .

[8]  Vincent Conitzer,et al.  Mixed-Integer Programming Methods for Finding Nash Equilibria , 2005, AAAI.

[9]  Jean Cardinal,et al.  Pricing of Geometric Transportation Networks , 2005, CCCG.

[10]  Sui Ruan,et al.  Patrolling in a Stochastic Environment , 2005 .

[11]  Gerald G. Brown,et al.  Defending Critical Infrastructure , 2006, Interfaces.

[12]  Vincent Conitzer,et al.  Computing the optimal strategy to commit to , 2006, EC '06.

[13]  Sarit Kraus,et al.  An efficient heuristic approach for security against multiple adversaries , 2007, AAMAS '07.

[14]  Sarit Kraus,et al.  Deployed ARMOR protection: the application of a game theoretic model for security at the Los Angeles International Airport , 2008, AAMAS.