Strategic Network Interdiction

We develop a strategic model of network interdiction in a non-cooperative game of flow. An adversary, endowed with a bounded quantity of bads, chooses a flow specifying a plan for carrying bads through a network from a base to a target. Simultaneously, an agency chooses a blockage specifying a plan for blocking the transport of bads through arcs in the network. The bads carried to the target cause a target loss while the blocked arcs cause a network loss. The adversary earns and the agency loses from both target loss and network loss. The adversary incurs the expense of carrying bads. In this model we study Nash equilibria and find a power law relation between the probability and the extent of the target loss. Our model contributes to the literature of game theory by introducing non-cooperative behavior into a Kalai-Zemel (cooperative) game of flow. Our research also advances models and results on network interdiction.Network Interdiction, Noncooperative Game of Flow, Nash Equilibrium, Power Law, Kalai-Zemel Game of Flow

Network Interdiction Using Adversarial Traffic Flows

Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios, such as stealth DoS attack, where the interdiction is performed through injecting adversarial traffic flows. Under this paradigm, we first study the deterministic flow interdiction problem, where the interdictor has perfect knowledge of the operation of network users. We show that the problem is highly inapproximable on general networks and is NP-hard even when the network is acyclic. We then propose an algorithm that achieves a logarithmic approximation ratio and quasi-polynomial time complexity for acyclic networks through harnessing the submodularity of the problem. Next, we investigate the robust flow interdiction problem, which adopts the robust optimization framework to capture the case where definitive knowledge of the operation of network users is not available. We design an approximation framework that integrates the aforementioned algorithm, yielding a quasi-polynomial time procedure with poly-logarithmic approximation ratio for the more challenging robust flow interdiction. Finally, we evaluate the performance of the proposed algorithms through simulations, showing that they can be efficiently implemented and yield near-optimal solutions

Network Interdiction under Uncertainty

We consider variants to one of the most common network interdiction formulations: the shortest path interdiction problem. This problem involves leader and a follower playing a zero-sum game over a directed network. The leader interdicts a set of arcs, and arc costs increase each time they are interdicted. The follower observes the leader\u27s actions and selects a shortest path in response. The leader\u27s optimal interdiction strategy maximizes the follower\u27s minimum-cost path. Our first variant allows the follower to improve the network after the interdiction by lowering the costs of some arcs, and the leader is uncertain regarding the follower\u27s cardinality budget restricting the arc improvements. We propose a multiobjective approach for this problem, with each objective corresponding to a different possible improvement budget value. To this end, we also present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem, and which tends to scale better than competing methods as the number of objectives grows. In our second variant, the leader selects a policy of randomized interdiction actions, and the follower uses the probability of where interdictions are deployed on the network to select a path having the minimum expected cost. We show that this continuous non-convex problem becomes strongly NP-hard when the cost functions are convex or when they are concave. After formally describing each variant, we present various algorithms for solving them, and we examine the efficacy of all our algorithms on test beds of randomly generated instances

Modeling Network Interdiction Tasks

Mission planners seek to target nodes and/or arcs in networks that have the greatest benefit for an operational plan. In joint interdiction doctrine, a top priority is to assess and target the enemy\u27s vulnerabilities resulting in a significant effect on its forces. An interdiction task is an event that targets the nodes and/or arcs of a network resulting in its capabilities being destroyed, diverted, disrupted, or delayed. Lessons learned from studying network interdiction model outcomes help to inform attack and/or defense strategies. A suite of network interdiction models and measures is developed to assist decision makers in identifying critical nodes and/or arcs to support deliberate and rapid planning and analysis. The interdiction benefit of a node or arc is a measure of the impact an interdiction task against it has on the residual network. The research objective is achieved with a two-fold approach. The measures approach begins with a network and uses node and/or arc measures to assess the benefit of each for interdiction. Concurrently, the models approach employs optimization models to explicitly determine the nodes and/or arcs that are most important to the planned interdiction task

Stochastic network interdiction games

Thesis (Ph.D.)--Boston UniversityNetwork interdiction problems consist of games between an attacker and an intelligent network, where the attacker seeks to degrade network operations while the network adapts its operations to counteract the effects of the attacker. This problem has received significant attention in recent years due to its relevance to military problems and network security. When the attacker's actions achieve uncertain effects, the resulting problems become stochastic network interdiction problems. In this thesis, we develop new algorithms for the solutions of different classes of stochastic network interdiction problems. We first focus on static network interdiction games where the attacker attacks the network once, which will change the network with certain probability. Then the network will maximize the flow from a given source to its destination. The attacker is seeking a strategy which minimizes the expected maximum flow after the attack. For this problem, we develop a new solution algorithm, based on parsimonious integration of branch and bound techniques with increasingly accurate lower bounds. Our method obtains solutions significantly faster than previous approaches in the literature. In the second part, we study a multi-stage interdiction problem where the attacker can attack the network multiple times, and observe the outcomes of its past attacks before selecting a current attack. For this dynamic interdiction game, we use a model-predictive approach based on a lower bound approximation. We develop a new set of performance bounds, which are integrated into a modified branch and bound procedure that extends the single stage approach to multiple stages. We show that our new algorithm is faster than other available methods with simulated experiments. In the last part, we study the nested information game between an intelligent network and an attacker, where the attacker has partial information about the network state, which refers to the availability of arcs. The attacker does not know the exact state, but has a probability distribution over the possible network states. The attacker makes several attempts to attack the network and observes the flows on the network. These observations will update the attacker's knowledge of the network and will be used in selecting the next attack actions. The defender can either send flow on that arc if it survived, or refrain from using it in order to deceive the attacker. For these problems, we develop a faster algorithm, which decomposes this game into a sequence of subgames and solves them to get the equilibrium strategy for the original game. Numerical results show that our method can handle large problems which other available methods fail to solve

Probability Distributions on Partially Ordered Sets and Network Interdiction Games

This article poses the following problem: Does there exist a probability distribution over subsets of a finite partially ordered set (poset), such that a set of constraints involving marginal probabilities of the poset's elements and maximal chains is satisfied? We present a combinatorial algorithm to positively resolve this question. The algorithm can be implemented in polynomial time in the special case where maximal chain probabilities are affine functions of their elements. This existence problem is relevant for the equilibrium characterization of a generic strategic interdiction game on a capacitated flow network. The game involves a routing entity that sends its flow through the network while facing path transportation costs, and an interdictor who simultaneously interdicts one or more edges while facing edge interdiction costs. Using our existence result on posets and strict complementary slackness in linear programming, we show that the Nash equilibria of this game can be fully described using primal and dual solutions of a minimum-cost circulation problem. Our analysis provides a new characterization of the critical components in the interdiction game. It also leads to a polynomial-time approach for equilibrium computation