Strategic Defense and Attack for Series and Parallel Reliability Systems: Comment

The contest-theoretic literature on the attack and defense of networks of targets focuses primarily on pure-strategy Nash equilibria. Hausken\u27s 2008 European Journal of Operational Research article typifies this approach, and many of the models in this literature either build upon this model or utilize similar techniques. We show that Hausken\u27s characterization of Nash equilibrium is invalid for much of the parameter space examined and provides necessary conditions for his solution to hold. The complete characterization of mixed-strategy equilibria remains an open problem, although there exist solutions in the literature for special prominent cases

Risk-attitude-based defense strategy considering proactive strike, preventive strike and imperfect false targets

This paper analyzes the optimal strategies for the attacker and the defender in an attack–defense game, considering the risk attitudes of both parties. The defender moves first, allocating its limited resources to three different measures: launching a proactive strike or preventive strike, building false targets, and protecting its genuine object. It is assumed that (a) launching a proactive strike has limited effectiveness on its rival and does not expose the genuine object itself, (b) a false target might be correctly identified as false, and (c) launching a preventive strike consumes less resources than a proactive strike and might expose the genuine object. The attacker moves after observing the defender's movements, allocating its limited resources to three measures: protecting its own base from a proactive strike or preventive strike, building false bases, and attacking the defender's genuine object. For each of the defender's given strategies, the attacker chooses the attack strategy that maximizes its cumulative prospect value, which accounts for the players’ risk attitudes. Similarly, the defender maximizes its cumulative prospect value by anticipating that the attacker will always choose the strategy combination that maximizes its own cumulative prospect value. Backward induction is used to obtain the optimal defense, attack strategies, and their corresponding cumulative prospect values. Our results show that the introduction of risk attitudes leads the game to a lose-lose situation under some circumstances and benefits one party in other cases

Defending simple series and parallel systems with imperfect false targets

10.1016/j.ress.2010.02.008Reliability Engineering and System Safety956679-688RESS

Locating and Protecting Facilities Subject to Random Disruptions and Attacks

Recent events such as the 2011 Tohoku earthquake and tsunami in Japan have revealed the vulnerability of networks such as supply chains to disruptive events. In particular, it has become apparent that the failure of a few elements of an infrastructure system can cause a system-wide disruption. Thus, it is important to learn more about which elements of infrastructure systems are most critical and how to protect an infrastructure system from the effects of a disruption. This dissertation seeks to enhance the understanding of how to design and protect networked infrastructure systems from disruptions by developing new mathematical models and solution techniques and using them to help decision-makers by discovering new decision-making insights. Several gaps exist in the body of knowledge concerning how to design and protect networks that are subject to disruptions. First, there is a lack of insights on how to make equitable decisions related to designing networks subject to disruptions. This is important in public-sector decision-making where it is important to generate solutions that are equitable across multiple stakeholders. Second, there is a lack of models that integrate system design and system protection decisions. These models are needed so that we can understand the benefit of integrating design and protection decisions. Finally, most of the literature makes several key assumptions: 1) protection of infrastructure elements is perfect, 2) an element is either fully protected or fully unprotected, and 3) after a disruption facilities are either completely operational or completely failed. While these may be reasonable assumptions in some contexts, there may exist contexts in which these assumptions are limiting. There are several difficulties with filling these gaps in the literature. This dissertation describes the discovery of mathematical formulations needed to fill these gaps as well as the identification of appropriate solution strategies