Deterrence and Risk Preferences in a Sequential Attacker-Defender Game with Continuous Defense Effort
Payyappalli, Vineet Madasseri
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Most attacker-defender games consider players as risk-neutral, whereas in reality attackers and defenders may be risk-seeking or risk-averse. This research studies the impact of players' risk preferences on their equilibrium behavior and their impact on the notion of deterrence. In particular, we study the effects of risk preferences by considering a single-period, sequential game where a defender has a continuous range of investment levels which could be strategically chosen to potentially deter an attack. In our context, defenders are governments and attackers are terrorist groups. This study presents some analytic results related to the effect of the attacker's and the defender's risk preferences on the defense effort and their effect on the optimal deterrence level. We show that the deterrence defense level increases in the attacker's initial wealth and risk preferences, but independent of the defender's risk preferences. This study provides insights that could be used by policy and decision makers involved in investment decisions in national security. Our model would also help in better interpretation of the large group of existing models which ignore players' risk preferences.