Strategic Network Interdiction

Games and Economic Behavior, 2009

We study the equilibria of non-atomic congestion games in which there are two types of players: rational players, who seek to minimize their own delay, and malicious players, who seek to maximize the average delay experienced by the rational players. We study the existence of pure and mixed Nash equilibria for these games, and we seek to quantify the impact of the malicious players on the equilibrium. One counterintuitive phenomenon which we demonstrate is the "windfall of malice": paradoxically, when a myopically malicious player gains control of a fraction of the flow, the new equilibrium may be more favorable for the remaining rational players than the previous equilibrium.

2017

Decision making in the context of crime execution and crime prevention can be successfully investigated with the implementation of game-theoretic tools. Evolutionary and mean-field game theory allow for the consideration of a large number of interacting players organized in social and behavioural structures, which typically characterize this context. Alternatively, `traditional' game-theoretic approaches can be applied for studying the security of an arbitrary network on a two player non-cooperative game. Theoretically underpinned by these instruments, in this thesis we formulate and analyse game-theoretic models of inspection, corruption, counter- terrorism, patrolling, and similarly interpreted paradigms. Our analysis suggests optimal strategies for the involved players, and illustrates the long term behaviour of the introduced systems. Our contribution is towards the explicit formulation and the thorough analysis of real life scenaria involving the security in network structu...

IIE Transactions, 2007

We consider a network interdiction problem on a multicommodity flow network, in which an attacker disables a set of network arcs in order to minimize the maximum profit that can be obtained from shipping commodities across the network. The attacker is assumed to have some budget for destroying (or "interdicting") arcs, and each arc is associated with a positive interdiction expense. In this paper, we examine problems in which interdiction must be discrete (i.e., each arc must either be left alone or completely destroyed), and in which interdiction can be continuous (the capacities of arcs may be partially reduced). For the discrete problem, we describe a linearized model for optimizing network interdiction that is similar to previous studies in the field, and compare it to a penalty model that does not require linearization constraints. For the continuous case, we prescribe an optimal partitioning algorithm along with a heuristic procedure for estimating the optimal objective function value. We demonstrate on a set of randomly generated test data that our penalty model for the discrete interdiction problem significantly reduces computational time when compared to that consumed by the linearization model.

Real-world attacks can be interpreted as the result of competitive interactions between networks, ranging from predator-prey networks to networks of countries under economic sanctions. Although the purpose of an attack is to damage a target network, it also curtails the ability of the attacker, which must choose the duration and magnitude of an attack to avoid negative impacts on its own functioning. Nevertheless, despite the large number of studies on interconnected networks, the consequences of initiating an attack have never been studied. Here, we address this issue by introducing a model of network competition where a resilient network is willing to partially weaken its own resilience in order to more severely damage a less resilient competitor. The attacking network can take over the competitor nodes after their long inactivity. However, due to a feedback mechanism the takeovers weaken the resilience of the attacking network. We define a conservation law that relates the feedback mechanism to the resilience dynamics for two competing networks. Within this formalism, we determine the cost and optimal duration of an attack, allowing a network to evaluate the risk of initiating hostilities.

2009

: Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. While developing an information network management system often encountered a situation where one should deal with malicious intrusion attempts aimed at obstructing the routing policy work. In this case, methods of networks management based on fluid models and a discrete controlled random walk model requires certain changes. In this work we propose an approach based on conflict control point of view that could be useful for modeling of attacking actions and response behaviour of the system.

Lecture Notes in Computer Science, 2009

The core of a cooperative game contains all stable distributions of a coalition's gains among its members. However, some games have an empty core, with every distribution being unstable. We allow an external party to offer a supplemental payment to the grand coalition, which may stabilize the game, if the payment is sufficiently high. We consider the cost of stability (CoS)-the minimal payment that stabilizes the game.

Mathematical Programming, 2007

We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behaviour. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to this cost. We define a generalized model, present characterizations of flows at Wardrop equilibria and prove bounds for the ratio of the social cost of a flow at Wardrop equilibrium over the cost when centralized coordination among users is allowed.

2018 Annual American Control Conference (ACC), 2018

This paper studies a special kind of equilibrium termed as "balanced equilibrium" which arises in the power allocation game defined in [15]. In equilibrium, each country in antagonism has to use all of its own power to counteract received threats, and the "threats" made to each adversary just balance out the threats received from that adversary. This paper establishes conditions on different types of networked international environments in order for this equilibrium to exist. The paper also links the existence of this type of equilibrium on structurally balanced graphs to the Hall's Maximum Matching problem and the Max Flow problem.

Algorithmica

Consider an information network with threats called attackers; each attacker uses a probability distribution to choose a node of the network to damage. Opponent to the attackers is a protector entity called defender; the defender scans and cleans from attacks some part of the network (in particular, a link), which it chooses independently using its own probability distribution. Each attacker wishes to maximize the probability of escaping its cleaning by the defender; towards a conflicting objective, the defender aims at maximizing the expected number of attackers it catches. We model this network security scenario as a non-cooperative strategic game on graphs. We are interested in its associated Nash equilibria, where no network entity can unilaterally increase its local objective. We obtain the following results: We obtain an algebraic characterization of (mixed) Nash equilibria. • No (non-trivial) instance of the graph-theoretic game has a pure Nash equilibrium. This is an immediate consequence of some covering properties we prove for the supports of the players in all (mixed) Nash equilibria. • We coin a natural subclass of mixed Nash equilibria, which we call Matching Nash equilibria, for this graph-theoretic game. Matching Nash equilibria are defined by enriching the necessary covering properties we proved with some additional conditions involving other structural parameters of graphs, such as Independent Sets. – We derive a characterization of graphs admitting Matching Nash equilibria. All such graphs have an Expanding Independent Set. The characterization enables a non-deterministic, polynomial time algorithm to compute a Matching Nash equilibrium for any such graph. – Bipartite graphs are shown to satisfy the characterization. So, using a polynomial time algorithm to compute a Maximum Matching for a bipartite graph, we obtain, as our main result, a deterministic, polynomial time algorithm to compute a Matching Nash equilibrium for any instance of the game with a bipartite graph.

2021

This paper studies a game of attack and interception in a network, where a single attacker chooses a target and a path, and each node chooses a level of protection. We show that the Nash equilibrium of the game exists and is unique. It involves a mixed strategy of the attacker except when one target has a very high value relative to others. We characterize equilibrium attack paths and attack distributions as a function of the underlying network and target values. We also show that adding a link or increasing the value of a target may harm the attacker a comparative statics effect which is reminiscent of Braess’s paradox in transportation economics. Finally, we contrast the Nash equilibrium with the equilibria of two variations of the model: one where nodes make sequential protection decisions upon observing the arrival of a suspicious object, and one where all nodes cooperate in defense.