Uniqueness of Equilibria in Interactive Networks

TL;DR

This paper generalizes a network model to include heterogeneous interactions and less restrictive conditions, establishing conditions for the existence and uniqueness of equilibria, and applies this to identify key players affecting systemic risk.

Contribution

It extends the unified network model to heterogeneous interaction functions with spectral radius constraints, proving equilibrium existence and uniqueness under broader conditions.

Findings

Equilibrium exists and is unique under new assumptions.

A measure to identify key players affecting systemic risk.

Application to systemic risk analysis in networks.

Abstract

This paper extends the unified network model, proposed by Acemoglu et al. (2016b), such that interaction functions can be heterogeneous, and the sensitivity matrix has less than or equal to one spectral radius. We show the existence and (almost surely) uniqueness of equilibrium under both eventually contracting and noncontracting assumptions. Applying the equilibrium in the study of systemic risk, we provide a measure to determine the key player who causes the most significant impact if removed from the network.