# Learning Deceptive Strategies in Adversarial Settings:
## 1 Introduction  
In adversarial multi-agent systems, agents often operate in environments characterized by partial observability, uncertainty, and dynamic interactions [1, 2, 3]. In such contexts, deception becomes a powerful strategic tool, allowing agents to obscure their true intentions and influence the behavior of opponents. In such environments, deception emerges as a powerful strategic tool, enabling agents to obscure their true intentions and influence the behavior of opponents. This capability is crucial across a range of domains--from deceiving radar systems [4] and manipulating speech or audio signals [5] to deceptive path planning for autonomous robots [6] and strategic information manipulation [7]. These diverse applications collectively demonstrate that misleading an adversary can substantially alter the outcome of interactions [8, 9, 10]. Consequently, there has been a renewed surge of research aimed at understanding and emulating deception in autonomous systems, particularly in the context of learning-enabled agents. However, modeling and learningdeceptive behavior in high-dimensional, multi-agent environments remain challenging due to the combinatorial complexity of agent interactions and the unpredictability of opponent strategies [11; 12; 13; 14; 15]. Previous research has addressed deception through classical game theory (e.g., [7]), optimal control (e.g., [16]), and multi-agent learning (e.g., [17]). Game-theoretic models have offered formal strategies for misleading opponents [18; 19] but often under rigid assumptions and limited scalability [20]. Reinforcement learning, particularly in multi-agent settings, has emerged as a promising framework for learning adaptive behavior from interactions [21; 22; 23; 24; 25]. Recent advances have applied value-based learning methods to explore deceptive behavior [26; 27], yet few works integrate game-theoretic reasoning with deep learning architectures in dynamic environments that feature multiple decoy goals and navigation constraints [28; 29; 30; 31]. Deception often arises from information asymmetry, where an agent with superior knowledge can manipulate agents with limited information into believing a false reality or forming incorrect beliefs. In this work, we specifically focus on a problem [29] characterized by inherent information asymmetry and investigate whether learning-enabled agents can exploit their information advantage to construct deceptive strategies. Additionally, we examine whether agents aware of their informational disadvantage can develop counter-deceptive strategies to avoid being misled. We propose a multi-agent learning framework guided by game-theoretic principles to address information and knowledge asymmetry among agents. The proposed game-theory-driven learning strategy offers several advantages over existing approaches to deception and counter-deception in multi-agent systems. First, by integrating game-theoretic reasoning directly into the learning process, our method allows agents to anticipate and strategically respond to the behavior of opponents, rather than relying solely on reactive or purely data-driven policies. This leads to more robust and interpretable strategies in adversarial settings. Second, the use of reward shaping informed by equilibrium concepts ensures that agents not only learn locally optimal behaviors but also align with globally coherent, stable outcomes. Unlike prior methods that often assume static environments or fixed opponent policies, our framework is designed to generalize across dynamic settings with changing goals, obstacle configurations, and opponent tactics. This adaptability enhances the strategic depth of the learned policies and improves sample efficiency during training. Finally, the integration of deception and counter-deception within a unified framework enables agents to both mislead and recognize deception, fostering richer and more resilient interactions in high-stakes domains such as autonomous security and multi-agent coordination.