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Most of the cybersecurity research focus on either presenting a specific vulnerability %or hacking technique, or proposing a specific defense algorithm to defend against a well-defined attack scheme. Although such cybersecurity research is important, few have paid attention to the dynamic interactions between attackers and defenders, where both sides are intelligent and will dynamically change their attack or defense strategies in order to gain the upper hand over their opponents. This 'cyberwar' phenomenon exists among most cybersecurity incidents in the real world, which warrants special research and analysis. In this paper, we propose a dynamic game theoretic framework (i.e., hyper defense) to analyze the interactions between the attacker and the defender as a non-cooperative security game. The key idea is to model attackers/defenders to have multiple levels of attack/defense strategies that are different in terms of effectiveness, strategy costs, and attack gains/damages. Each player adjusts his strategy based on the strategy's cost, potential attack gain/damage, and effectiveness in anticipating of the opponent's strategy. We study the achievable Nash equilibrium for the attacker-defender security game where the players employ an efficient strategy according to the obtained equilibrium. Furthermore, we present case studies of three different types of network attacks and put forth how our hyper defense system can successfully model them. Simulation results show that the proposed game theoretical system achieves a better performance compared to two other fixed-strategy defense systems.