The Architecture of Illusion: Network Opacity and Strategic Escalation

2026-02-10

AI Summary

This study addresses how individuals with bounded rationality form beliefs about others’ cognitive abilities in information-constrained networked environments. The authors propose the “Connected Minds” model, which integrates iterative reasoning with biased observations shaped by agents’ network positions, unifying the Level-k and cognitive hierarchy frameworks through a transparency parameter \( p \). The model identifies a “sophistication bias” induced by network opacity and introduces the “escalation principle” and “transparency reversal” mechanisms. Theoretical analysis reveals that reducing transparency enhances aggregate effort in strategic complementarity games, whereas increasing transparency stabilizes equilibria in coordination games. This work provides a network-structure-based foundation for mechanism design in platform information architecture.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Reasoning with Beliefs

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• bounded rationality
• network opacity
• cognitive hierarchy
• strategic escalation
• information bias

Innovation

• network opacity
• iterative reasoning
• sophisticated bias
• mechanism design
• cognitive hierarchy