We study strategic interaction in linear-quadratic network games where agents act on subjective, misspecified models of their environment. Agents observe noisy aggregate signals generated by local network externalities and interpret them through simplified conjectures, such as constant or mean-field representations. We characterize the long-run behavior using the Berk-Nash equilibrium (BNE) concept, establishing conditions under which BNE diverges from the Nash equilibrium of the perfectly specified game. We quantify this divergence using a Value of Misspecification (VoM) metric. Building on this framework, we introduce "cognitive arbitrage" -- a design paradigm where a system designer strategically shapes agents' conjectures via minimal observation distortions to steer equilibrium outcomes. We formulate the cognitive arbitrage problem as a Stackelberg optimization with closed-form solutions and prove the convergence of a two-time-scale learning algorithm to the optimal BNE. Our results provide a principled framework for influencing behavior in networked systems with bounded rationality, offering a new perspective on mechanism design that operates on agents' representations rather than their incentives.

翻译：本文研究线性二次网络博弈中的策略互动，其中智能体基于对环境的主观错误设定模型采取行动。智能体观察由局部网络外部性产生的噪声聚合信号，并通过简化猜想（如常数或平均场表示）对其进行解释。我们使用伯克-纳什均衡（BNE）概念刻画长期行为，建立了BNE与完全设定博弈的纳什均衡发生偏离的条件。我们通过错误设定价值（VoM）度量量化这种偏离。基于此框架，我们提出"认知套利"——一种系统设计者通过最小化观测失真策略性地塑造智能体猜想以引导均衡结果的设计范式。我们将认知套利问题构建为具有闭式解的斯塔克尔伯格优化问题，并证明双时间尺度学习算法向最优BNE的收敛性。研究结果为有限理性网络系统中的行为影响提供了理论框架，为机制设计提供了从智能体表征而非激励角度出发的新视角。