Stackelberg security game models and associated computational tools have seen deployment in a number of high-consequence security settings, such as LAX canine patrols and Federal Air Marshal Service. These models focus on isolated systems with only one defender, despite being part of a more complex system with multiple players. Furthermore, many real systems such as transportation networks and the power grid exhibit interdependencies between targets and, consequently, between decision makers jointly charged with protecting them. To understand such multidefender strategic interactions present in security, we investigate game theoretic models of security games with multiple defenders. Unlike most prior analysis, we focus on the situations in which each defender must protect multiple targets, so that even a single defender's best response decision is, in general, highly non-trivial. We start with an analytical investigation of multidefender security games with independent targets, offering an equilibrium and price-of-anarchy analysis of three models with increasing generality. In all models, we find that defenders have the incentive to over-protect targets, at times significantly. Additionally, in the simpler models, we find that the price of anarchy is unbounded, linearly increasing both in the number of defenders and the number of targets per defender. Considering interdependencies among targets, we develop a novel mixed-integer linear programming formulation to compute a defender's best response, and make use of this formulation in approximating Nash equilibria of the game. We apply this approach towards computational strategic analysis of several models of networks representing interdependencies, including real-world power networks. Our analysis shows how network structure and the probability of failure spread determine the propensity of defenders to over- or under-invest in security.
Another somewhat related line of work considers the problem of coordination and teamwork among multiple defenders in a purely cooperative setting @cite_3 @cite_2 . This work, however, is entirely unlike ours: in particular, our primary focus is on the impact of among the defenders with different (though certainly related) motivations, rather than coordination issues and teamwork. While often effective coordination among multiple defenders can be achieved, just as often (if not predominantly) decentralization of decision making processes and resources inherently give rise to distinct, and often conflicting, incentives among defenders.
@cite_3 @cite_2
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We study security games with multiple defenders. To achieve maximum security, defenders must perfectly synchronize their randomized allocations of resources. However, in real-life scenarios (such as protection of the port of Boston) this is not the case. Our goal is to quantify the loss incurred by miscoordination between defenders, both theoretically and empirically. We introduce two notions that capture this loss under different assumptions: the price of miscoordination, and the price of sequential commitment. Generally speaking, our theoretical bounds indicate that the loss may be extremely high in the worst case, while our simulations establish a smaller yet significant loss in practice. Objective: We conducted an empirical analysis of human teamwork to investigate the ways teammates incorporate coordination behaviors, including verbal and nonverbal cues, into their action planning. Background: In space, military, aviation, and medical industries, teams of people effectively coordinate to perform complex tasks under stress induced by uncertainty, ambiguity, and time pressure. As robots increasingly are introduced into these domains, we seek to understand effective human-team coordination to inform natural and effective human-robot coordination. Method: We conducted teamwork experiments in which teams of two people performed a complex task, involving ordering, timing, and resource constraints. Half the teams performed under time pressure, and half performed without time pressure. We cataloged the coordination behaviors used by each team and analyzed the speed of response and specificity of each coordination behavior. Results: Analysis shows that teammates respond to explicit cues, includin... In typical multiagent teamwork settings, the teammates are either programmed together, or are otherwise provided with standard communication languages and coordination protocols. In contrast, this paper presents an ad hoc team setting in which the teammates are not pre-coordinated, yet still must work together in order to achieve their common goal(s). We represent a specific instance of this scenario, in which a teammate has limited action capabilities and a fixed and known behavior, as a finite-horizon, cooperative k-armed bandit. In addition to motivating and studying this novel ad hoc teamwork scenario, the paper contributes to the k-armed bandits literature by characterizing the conditions under which certain actions are potentially optimal, and by presenting a polynomial dynamic programming algorithm that solves for the optimal action when the arm payoffs come from a discrete distribution. We study a spectrum sharing problem in an unlicensed band where multiple systems coexist and interfere with each other. We first analyze a cooperative setting where all the systems collaborate to achieve a common goal. Under the assumptions that the systems communicate with Gaussian signals and treat interference as noise, we study the structure of the optimal power allocations. We show that any Pareto efficient vector of rates can be achieved with piece-wise constant power allocations. Moreover, if a strong interference condition among all the systems is satisfied, we show that frequency division multiplexing is optimal. We then consider a non-cooperative situation, where the systems act in a selfish and rational way, and investigate how the lack of cooperation can affect performance. Using game theory, we first analyze the possible outcomes of a one shot game, and observe that in many cases an inefficient solution results. We show that by extending the game definition to that of a repeated game, the possibility of building reputations and applying punishments allows to enlarge the set of achievable rates. We present examples that show that in many cases, the performance loss due to lack of cooperation is small. We also provide a converse theorem that proves that our results are tight and quantify the best achievable performance in a non-cooperative scenario