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Register a new userContinuous Patrolling Games
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Thomas Lidbetter Dr
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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The continuous patrolling game studied here was first proposed in Alpern et al. (2011), which studied a discrete time game where facilities to be protected were modeled as the nodes of a graph. Here we consider protecting roads or pipelines, modeled as the arcs of a continuous network $Q$. The Attacker chooses a point of $Q$ to attack during a chosen time interval of fixed duration (the attack time, $alpha$). The Patroller chooses a unit speed path on $Q$ and intercepts the attack (and wins) if she visits the attacked point during the attack time interval. Solutions to the game have previously been given in certain special cases. Here, we analyze the game on arbitrary networks. Our results include the following: (i) a solution to the game for any network $Q$, as long as $alpha$ is sufficiently short, generalizing the known solutions for circle or Eulerian networks and the network with two nodes joined by three arcs; (ii) a solution to the game for all tree networks that satisfy a condition on their extremities. We present a conjecture on the solution of the game for arbitrary trees and establish it in certain cases.
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Security Games employ game theoretical tools to derive resource allocation strategies in security domains. Recent works considered the presence of alarm systems, even suffering various forms of uncertainty, and showed that disregarding alarm signals may lead to arbitrarily bad strategies. The central problem with an alarm system, unexplored in other Security Games, is finding the best strategy to respond to alarm signals for each mobile defensive resource. The literature provides results for the basic single-resource case, showing that even in that case the problem is computationally hard. In this paper, we focus on the challenging problem of designing algorithms scaling with multiple resources. First, we focus on finding the minimum number of resources assuring non-null protection to every target. Then, we deal with the computation of multi-resource strategies with different degrees of coordination among resources. For each considered problem, we provide a computational analysis and propose algorithmic methods.
We focus on adversarial patrolling games on arbitrary graphs, where the Defender can control a mobile resource, the targets are alarmed by an alarm system, and the Attacker can observe the actions of the mobile resource of the Defender and perform different attacks exploiting multiple resources. This scenario can be modeled as a zero-sum extensive-form game in which each player can play multiple times. The game tree is exponentially large both in the size of the graph and in the number of attacking resources. We show that when the number of the Attackers resources is free, the problem of computing the equilibrium path is NP-hard, while when the number of resources is fixed, the equilibrium path can be computed in poly-time. We provide a dynamic-programming algorithm that, given the number of the Attackers resources, computes the equilibrium path requiring poly-time in the size of the graph and exponential time in the number of the resources. Furthermore, since in real-world scenarios it is implausible that the Defender knows the number of attacking resources, we study the robustness of the Defenders strategy when she makes a wrong guess about that number. We show that even the error of just a single resource can lead to an arbitrary inefficiency, when the inefficiency is defined as the ratio of the Defenders utilities obtained with a wrong guess and a correct guess. However, a more suitable definition of inefficiency is given by the difference of the Defenders utilities: this way, we observe that the higher the error in the estimation, the higher the loss for the Defender. Then, we investigate the performance of online algorithms when no information about the Attackers resources is available. Finally, we resort to randomized online algorithms showing that we can obtain a competitive factor that is twice better than the one that can be achieved by any deterministic online algorithm.
Green Security Games (GSGs) have been successfully used in the protection of valuable resources such as fisheries, forests and wildlife. While real-world deployment involves both resource allocation and subsequent coordinated patrolling with communication and real-time, uncertain information, previous game models do not fully address both of these stages simultaneously. Furthermore, adopting existing solution strategies is difficult since they do not scale well for larger, more complex variants of the game models. We therefore first propose a novel GSG model that combines defender allocation, patrolling, real-time drone notification to human patrollers, and drones sending warning signals to attackers. The model further incorporates uncertainty for real-time decision-making within a team of drones and human patrollers. Second, we present CombSGPO, a novel and scalable algorithm based on reinforcement learning, to compute a defender strategy for this game model. CombSGPO performs policy search over a multi-dimensional, discrete action space to compute an allocation strategy that is best suited to a best-response patrolling strategy for the defender, learnt by training a multi-agent Deep Q-Network. We show via experiments that CombSGPO converges to better strategies and is more scalable than comparable approaches. Third, we provide a detailed analysis of the coordination and signaling behavior learnt by CombSGPO, showing group formation between defender resources and patrolling formations based on signaling and notifications between resources. Importantly, we find that strategic signaling emerges in the final learnt strategy. Finally, we perform experiments to evaluate these strategies under different levels of uncertainty.
We present a family of nonlocal games in which the inputs the players receive are continuous. We study three representative members of the family. For the first two a team sharing quantum correlations (entanglement) has an advantage over any team restricted to classical correlations. We conjecture that this is true for the third member of the family as well.
In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to nearby games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games.
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