Cognitive vulnerabilities shape human decision-making and arise primarily from two sources: (1) cognitive capabilities, which include disparities in knowledge, education, expertise, or access to information, and (2) cognitive biases, such as rational inattention, confirmation bias, and base rate neglect, which influence how individuals perceive and process information. Exploiting these vulnerabilities allows an entity with superior cognitive awareness to gain a strategic advantage, a concept referred to as cognitive arbitrage. This paper investigates how to exploit the cognitive vulnerabilities of Advanced Persistent Threat (APT) attackers and proposes cognition-aware defenses that leverage windows of superiority to counteract attacks. Specifically, the proposed bi-level cyber warfare game focuses on "strategic-level" design for defensive deception mechanisms, which then facilitates "operational-level" actions and tactical-level execution of Tactics, Techniques, and Procedures (TTPs). Game-theoretic reasoning and analysis play a significant role in the cross-echelon quantitative modeling and design of cognitive arbitrage strategies. Our numerical results demonstrate that although the defender's initial advantage diminishes over time, strategically timed and deployed deception techniques can turn a negative value for the attacker into a positive one during the planning phase, and achieve at least a 40% improvement in total rewards during execution. This demonstrates that the defender can amplify even small initial advantages, sustain a strategic edge over the attacker, and secure long-term objectives, such as protecting critical assets throughout the attacker's lifecycle.