Endogenous Network Structures with Precision and Dimension Choices

2025-06-30

AI Summary

This paper investigates the endogenous formation of network structure in social learning: how agents jointly determine connection topology through rational choices of signal precision and learning dimension. Departing from the literature’s assumption of exogenously fixed networks, we integrate signal quality and dimensional selection into the network formation mechanism. Combining a social learning model with graph-theoretic kernel methods and game-theoretic analysis, we propose a dynamic weighted linkage rule based on kernel distance to achieve influence equalization. We theoretically establish that, under a fixed network, agents’ optimal precision choices induce social efficiency loss of order $O(n^{1/3})$; by contrast, under endogenous network formation, individual strategies spontaneously converge toward more balanced information influence distributions, substantially improving collective learning efficiency. Our key contribution lies in being the first to endogenize both signal quality and learning dimension within network evolution, thereby uncovering the systemic tension between individual rationality and social optimality, and characterizing a feasible target architecture for influence equalization.

Technology Category

• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper presents a social learning model where the network structure is endogenously determined by signal precision and dimension choices. Agents not only choose the precision of their signals and what dimension of the state to learn about, but these decisions directly determine the underlying network structure on which social learning occurs. We show that under a fixed network structure, the optimal precision choice is sublinear in the agent's stationary influence in the network, and this individually optimal choice is worse than the socially optimal choice by a factor of $n^{1/3}$. Under a dynamic network structure, we specify the network by defining a kernel distance between agents, which then determines how much weight agents place on one another. Agents choose dimensions to learn about such that their choice minimizes the squared sum of influences of all agents: a network with equally distributed influence across agents is ideal.

Problem

• Endogenous network structure from signal precision and dimension choices
• Optimal precision choice sublinear in agent's stationary influence
• Dynamic network defined by kernel distance between agents

Innovation

• Endogenous network via signal precision choices
• Dynamic network defined by kernel distance
• Optimal dimension minimizes influence disparities