On the Difficulty of Characterizing Network Formation with Endogenous Behavior

TL;DR

This paper critiques a previous model of network formation with strategic agents, revealing errors in the characterization of stable networks and discussing the implications for understanding endogenous network structures.

Contribution

It identifies a flaw in Bolletta's characterization of Nash stable networks, providing a counterexample and clarifying the complexities in modeling endogenous network formation.

Findings

Counterexample disproves the claimed network structure

Highlights errors in previous analytical approach

Discusses implications for future network formation models

Abstract

Bolletta (2021, Math. Soc. Sci. 114:1-10) studies a model in which a network is strategically formed and then agents play a linear best-response investment game in it. The model is motivated by an application in which people choose both their study partners and their levels of educational effort. Agents have different one-dimensional types $\unicode{x2013}$ private returns to effort. A main result claims that pairwise Nash stable networks have a locally complete structure consisting of possibly overlapping cliques: if two agents are linked, they are part of a clique composed of all agents with types between theirs. We offer a counterexample showing that the claimed characterization is incorrect, highlight where the analysis errs, and discuss implications for network formation models.