Deception in Target Defense Game with Unknown Attackers Speed within a Continuous Range

In this paper, a target defense game involving one Defender and two Attackers is investigated. The Defender, constrained within a specified range, strives to capture as many Attackers as possible by aligning itself with them before they reach the unit circle target, while the Attackers aim to reach the target without being captured. Different from the information structure setups in existing literatures, this paper introduces an asymmetry in information: the maximum speed of the Attackers, which is publicly known to lie within a continuous range, is not revealed to the Defender. To explore whether deception can be implemented by the Attackers through leveraging their information advantage, a critical speed analysis framework is developed to resolve the challenge of infinite possible speeds available to the Attackers. This framework establishes the sufficient and necessary condition for a mismatching direction scenario, in which no Defender strategy can guarantee an optimal payoff across all possible Attacker speeds. Furthermore, our analysis identifies specific dilemma conditions that compel the Defender to make uncertain guesses. Notably, it is demonstrated that by adopting a proposed slow-speed, information-limiting strat egy, the Attackers can mislead the Defender into making incorrect decisions, thereby achieving a better payoff compared to employing a maximum capability strategy under complete information. The simulation results further illustrate the dilemma conditions and provide representative examples to visualize the outcomes.