Local Weak Limits for Equilibrium and Risk in Economic Networks

Hamed Amini and Zhecheng Wu

Papers from arXiv.org

Abstract: We study equilibrium and risk evaluation in large sparse economic networks with heterogeneous responses, shocks, and bilateral exposures. Our approach approximates the distribution of equilibrium outcomes through local computations on a limiting rooted network. Under marked local weak convergence, we prove convergence in probability of the empirical equilibrium distribution in two settings: uniformly contractive responses and bounded monotone nonexpansive responses whose lower and upper root iterations coalesce. In the latter setting, the limit is independent of the measurable finite-network equilibrium selection, even when equilibria are not unique. Under bounded domain and continuity assumptions, this convergence extends to law-invariant risk measures, including conditional value-at-risk, with recursion-depth error bounds under additional regularity. Numerical experiments on production networks and payment clearing systems illustrate the accuracy and computational benefits of the local approximation.

Date: 2026-09
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