The Architecture of Illusion: Network Opacity and Strategic Escalation

TL;DR

This paper introduces the Connected Minds model, unifying bounded rationality frameworks by incorporating network bias and opacity, revealing how transparency influences strategic behavior and equilibrium outcomes.

Contribution

It develops a unified model linking Cognitive Hierarchy and Level-k theories through network opacity, and derives mechanisms to control strategic escalation via transparency adjustments.

Findings

Network opacity causes overestimation of opponents' cognitive depth.

Transparency levels influence effort and coordination in strategic games.

Model provides actionable insights for designing information disclosure policies.

Abstract

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.