Modeling costly learning and counter-learning in a defender-attacker game with private defender information

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• 作者：Jie Xu ; Jun Zhuang
• 关键词：Defender ; attacker games ; Costly learning ; Counter ; learning ; Game theory ; Value of perfect information ; Value of imperfect information
• 刊名：Annals of Operations Research
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：236
• 期：1
• 页码：271-289
• 全文大小：1,161 KB
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• 作者单位：Jie Xu (1)
  Jun Zhuang (1)
  
  1. Department of Industrial and System Engineering, SUNY at Buffalo, Buffalo, NY, 14260, USA
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Combinatorics
  Theory of Computation
  
• 出版者：Springer Netherlands
• ISSN：1572-9338

文摘

In asymmetric war scenarios (e.g., counter-terrorism), the adversary usually invests a significant time to learn the system structure and identify vulnerable components, before launching attacks. Traditional game-theoretic defender-attacker models either ignore such learning periods or the entailed costs. This paper fills the gap by analyzing the strategic interactions of the terrorist’s costly learning and defender’s counter-learning and defense strategies in a game with private defender information. Our model allows six possible attacker strategies: (a) attack immediately; (b) learn and attack; (c) learn and not attack; (d) learn and attack when appearing vulnerable and not attack when appearing invulnerable; (e) learn and not attack when appearing vulnerable and attack when appearing invulnerable; and (f) not attack. Our results show that four of the six strategies (a, d, e, f) are possible at equilibrium and the other two (b, c) are strictly dominated. Interestingly, we find that the counterintuitive strategy (e) could be at equilibrium, especially when the probability that the target appears vulnerable given it is invulnerable is sufficiently high. Our results also show that the attacker’s learning cost has a significant impact on both the attacker’s best responses and the defender’s equilibrium deception and defense strategies. Finally, we study the attacker’s values of perfect information and imperfect information, which provide additional insights for defense and counter-learning strategies.