Deterrence and Risk Preferences in Sequential Attacker-Defender Games with Continuous Efforts.

Most attacker-defender games consider players as risk neutral, whereas in reality attackers and defenders may be risk seeking or risk averse. This article studies the impact of players' risk preferences on their equilibrium behavior and its effect on the notion of deterrence. In particular, we study the effects of risk preferences in a single-period, sequential game where a defender has a continuous range of investment levels that could be strategically chosen to potentially deter an attack. This article presents analytic results related to the effect of attacker and defender risk preferences on the optimal defense effort level and their impact on the deterrence level. Numerical illustrations and some discussion of the effect of risk preferences on deterrence and the utility of using such a model are provided, as well as sensitivity analysis of continuous attack investment levels and uncertainty in the defender's beliefs about the attacker's risk preference. A key contribution of this article is the identification of specific scenarios in which the defender using a model that takes into account risk preferences would be better off than a defender using a traditional risk-neutral model. This study provides insights that could be used by policy analysts and decisionmakers involved in investment decisions in security and safety.

Modeling Resources Allocation in Attacker-Defender Games with "Warm Up" CSF.

Like many other engineering investments, the attacker's and defender's investments may have limited impact without initial capital to "warm up" the systems. This article studies such "warm up" effects on both the attack and defense equilibrium strategies in a sequential-move game model by developing a class of novel and more realistic contest success functions. We first solve a single-target attacker-defender game analytically and provide numerical solutions to a multiple-target case. We compare the results of the models with and without consideration of the investment "warm up" effects, and find that the defender would suffer higher expected damage, and either underestimate the attacker effort or waste defense investment if the defender falsely believes that no investment "warm up" effects exist. We illustrate the model results with real data, and compare the results of the models with and without consideration of the correlation between the "warm up" threshold and the investment effectiveness. Interestingly, we find that the defender is suggested to give up defending all the targets when the attack or the defense "warm up" thresholds are sufficiently high. This article provides new insights and suggestions on policy implications for homeland security resource allocation.