Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Beijing, 100190, China.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China.
Sci Rep. 2023 Jul 12;13(1):11308. doi: 10.1038/s41598-023-38460-8.
In a stochastic Stackelberg asymmetric security game, the strong Stackelberg equilibrium (SSE) strategy is a popular option for the defender to get the highest utility against an attacker with the best response (BR) strategy. However, the attacker may be a boundedly rational player, who adopts a combination of the BR strategy and a fixed stubborn one. In such a condition, the SSE strategy may not maintain the defensive performance due to the stubbornness. In this paper, we focus on how the defender can adopt the unilateral-control zero-determinate (ZD) strategy to confront the boundedly rational attacker. At first, we verify the existence of ZD strategies for the defender. We then investigate the performance of the defender's ZD strategy against a boundedly rational attacker, with a comparison of the SSE strategy. Specifically, when the attacker's strategy is close to the BR strategy, the ZD strategy admits a bounded loss for the defender compared with the SSE strategy. Conversely, when the attacker's strategy is close to the stubborn strategy, the ZD strategy can bring higher defensive performance for the defender than the SSE strategy does.
在随机 Stackelberg 非对称安全博弈中，强 Stackelberg 均衡（SSE）策略是防御者针对采用最佳响应（BR）策略的攻击者获得最高效用的热门选择。然而，攻击者可能是有限理性的参与者，他采用 BR 策略和固定固执策略的组合。在这种情况下，由于固执，SSE 策略可能无法保持防御性能。在本文中，我们专注于防御者如何采用单边控制零确定（ZD）策略来应对有限理性的攻击者。首先，我们验证了防御者的 ZD 策略的存在性。然后，我们研究了防御者 ZD 策略对有限理性攻击者的性能，与 SSE 策略进行了比较。具体来说，当攻击者的策略接近 BR 策略时，ZD 策略相对于 SSE 策略允许防御者承受有界损失。相反，当攻击者的策略接近固执策略时，ZD 策略可以为防御者带来比 SSE 策略更高的防御性能。
