幻觉的架构：网络不透明与战略升级
The Architecture of Illusion: Network Opacity and Strategic Escalation
AI总结：
本文提出'联结心智'模型，通过参数化网络偏见统一有限理性框架，揭示网络不透明性如何引发复杂偏见并影响战略行为，提出升级原理与透明度反转，展现网络拓扑对认知行为的调节作用。
摘要：
传统的有限理性模型通常假设代理人要么准确了解群体的推理能力（认知层次）要么持有固执的、退化的信念（第k层）。我们引入了“联结心智”模型，通过整合迭代推理与参数化网络偏见来统一这些框架。我们提出，代理人并不观察整个群体；而是观察一个受其网络位置偏倚的样本，由局部参数p决定，代表算法排名、社会同质性或信息披露。我们证明该参数充当连续桥梁：当网络变得不透明（p→0）时，模型退化为我的opic第k层递归；当网络完全透明（p=1）时，恢复标准的认知层次模型。理论上，我们证明网络不透明引发一种“复杂偏见”，使代理人系统性地高估对手的认知深度，同时保持信念分布的对数凹性。这使p成为可操作的杠杆：规划者或平台可以调节透明度，全局或按段（个性化p_k）来塑造均衡行为。从机制设计角度看，我们推导出“升级原理”：在战略互补游戏中，限制信息可以最大化总体努力，通过将代理人困在回声室中，使他们与幻觉中的高复杂度对手竞争。相反，我们发现协调游戏中存在“透明度反转”，其中最大化网络可见性是减少方差和稳定结果的必要条件。我们的结果表明，网络拓扑结构作为一种认知变焦透镜，决定代理人是作为本地模仿者还是全局优化者行为。
英文摘要：
Standard models of bounded rationality typically assume agents either possess accurate knowledge of the population's reasoning abilities (Cognitive Hierarchy) or hold dogmatic, degenerate beliefs (Level-$k$). We introduce the ``Connected Minds'' model, which unifies these frameworks by integrating iterative reasoning with a parameterized network bias. We posit that agents do not observe the global population; rather, they observe a sample biased by their network position, governed by a locality parameter $p$ representing algorithmic ranking, social homophily, or information disclosure. We show that this parameter acts as a continuous bridge: the model collapses to the myopic Level-$k$ recursion as networks become opaque ($p \to 0$) and recovers the standard Cognitive Hierarchy model under full transparency ($p=1$). Theoretically, we establish that network opacity induces a \emph{Sophisticated Bias}, causing agents to systematically overestimate the cognitive depth of their opponents while preserving the log-concavity of belief distributions. This makes $p$ an actionable lever: a planner or platform can tune transparency, globally or by segment (a personalized $p_k$), to shape equilibrium behavior. From a mechanism design perspective, we derive the \emph{Escalation Principle}: in games of strategic complements, restricting information can maximize aggregate effort by trapping agents in echo chambers where they compete against hallucinated, high-sophistication peers. Conversely, we identify a \emph{Transparency Reversal} for coordination games, where maximizing network visibility is required to minimize variance and stabilize outcomes. Our results suggest that network topology functions as a cognitive zoom lens, determining whether agents behave as local imitators or global optimizers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
