A Memetic Approach for Sequential Security Games on a Plane with Moving Targets

Abstract

This paper introduces a new type of Security Games (SG) played on a plane with targets moving along predefined straight line trajectories and its respective Mixed Integer Linear Programming (MILP) formulation. Three approaches for solving the game are proposed and experimentally evaluated: application of an MILP solver to finding exact solutions for small-size games, MILP-based extension of recently published zero-sum SG approach to the case of generalsum games for finding approximate solutions of medium-size games, and the use of Memetic Algorithm (MA) for mediumsize and large-size game instances, which are beyond MILP’s scalability. Utilization of MA is, to the best of our knowledge, a new idea in the field of SG. The novelty of proposed solution lies specifically in efficient chromosome-based game encoding and dedicated local improvement heuristics. In vast majority of test cases with known equilibrium profiles, the method leads to optimal solutions with high stability and approximately linear time scalability. Another advantage is an iteration-based construction of the system, which makes the approach essentially an anytime method. This property is of paramount importance in case of restrictive time limits, which could hinder the possibility of calculating an exact solution. On a general note, we believe that MA-based methods may offer a viable alternative to MILP solvers for complex games that require application of approximate solving methods.

Anchoring Theory in Sequential Stackelberg Games

“…The other heuristic method applicable to sequential SGs considered in this paper [34] utilizes EA to find the leader's mixed strategy and, to our knowledge, is the first generic evolutionary approach proposed in this domain. We are aware of only one other application of EAs to solving sequential SGs [12] which, however, is specifically designed to games on a plane with moving targets. EASG follows a standard evolutionary algorithm scheme and is presented in Algorithm 1.…”

“…At the same time, in reference to large-scale sequential SGs, several algorithms utilizing different techniques, e.g. sequence-form [2], correlated equilibria [4], game abstraction [5], Evolutionary Algorithm [12,34] or Monte Carlo sampling [10,13] which visibly extended the range of tractable SGs, have been proposed recently.…”

“…marginal probability p(σ f ) ∈ {0, 1} (*)). In the above ATSG version of C2016, defined by equations ( 11) - (12), conditions (*) may not initially hold for all σ f , but must be all fulfilled at completion of C2016, since they constitute a stopping condition of this method.…”

Minimizing Expected Intrusion Detection Time in Adversarial Patrolling

“…The first approach suffers from scalability issues caused by non-linear constraints [5,6]. Reinforcement learning has so far been successful mainly for patrolling with finite horizon, such as green security games [10,20,34,35]. Gradient descent techniques for finite-memory strategies [22,23,25] are applicable to patrolling graphs of reasonable size.…”

Learning Attacker's Bounded Rationality Model in Security Games

“…EASG is designed as a general framework that can be easily adapted to various types of SG. There are also heuristic methods devoted to particular SG formulations [22].…”