Equilibria and Systemic Risk in Saturated Networks
(2022) In Mathematics of Operations Research 47(3). p.1781-1801- Abstract
- We undertake a fundamental study of network equilibria modeled as solutions of fixed-point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations. It is one of the simplest continuous models accounting for shock propagation phenomena and cascading failure effects. This model also characterizes Nash equilibria of constrained quadratic network games with strategic complementarities. We first derive explicit expressions for network equilibria and prove necessary and sufficient conditions for their uniqueness, encompassing and generalizing results available in the literature.... (More)
- We undertake a fundamental study of network equilibria modeled as solutions of fixed-point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations. It is one of the simplest continuous models accounting for shock propagation phenomena and cascading failure effects. This model also characterizes Nash equilibria of constrained quadratic network games with strategic complementarities. We first derive explicit expressions for network equilibria and prove necessary and sufficient conditions for their uniqueness, encompassing and generalizing results available in the literature. Then, we study jump discontinuities of the network equilibria when the exogenous flows cross certain regions of measure 0 representable as graphs of continuous functions. Finally, we discuss some implications of our results in the two main motivating applications. In financial networks, this bifurcation phenomenon is responsible for how small shocks in the assets of a few nodes can trigger major aggregate losses to the system and cause the default of several agents. In constrained quadratic network games, it induces a blow-up behavior of the sensitivity of Nash equilibria with respect to the individual benefits. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/96dec4d7-ad9f-4a17-a80f-ffb4a0787365
- author
- Massai, Leonardo ; Como, Giacomo LU and Fagnani, Fabio
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Mathematics of Operations Research
- volume
- 47
- issue
- 3
- pages
- 1781 - 1801
- publisher
- INFORMS Institute for Operations Research and the Management Sciences
- external identifiers
-
- scopus:85140014625
- ISSN
- 0364-765X
- DOI
- 10.1287/moor.2021.1188
- language
- English
- LU publication?
- yes
- id
- 96dec4d7-ad9f-4a17-a80f-ffb4a0787365
- date added to LUP
- 2022-02-14 17:37:05
- date last changed
- 2025-04-04 14:23:36
@article{96dec4d7-ad9f-4a17-a80f-ffb4a0787365,
abstract = {{We undertake a fundamental study of network equilibria modeled as solutions of fixed-point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations. It is one of the simplest continuous models accounting for shock propagation phenomena and cascading failure effects. This model also characterizes Nash equilibria of constrained quadratic network games with strategic complementarities. We first derive explicit expressions for network equilibria and prove necessary and sufficient conditions for their uniqueness, encompassing and generalizing results available in the literature. Then, we study jump discontinuities of the network equilibria when the exogenous flows cross certain regions of measure 0 representable as graphs of continuous functions. Finally, we discuss some implications of our results in the two main motivating applications. In financial networks, this bifurcation phenomenon is responsible for how small shocks in the assets of a few nodes can trigger major aggregate losses to the system and cause the default of several agents. In constrained quadratic network games, it induces a blow-up behavior of the sensitivity of Nash equilibria with respect to the individual benefits.}},
author = {{Massai, Leonardo and Como, Giacomo and Fagnani, Fabio}},
issn = {{0364-765X}},
language = {{eng}},
number = {{3}},
pages = {{1781--1801}},
publisher = {{INFORMS Institute for Operations Research and the Management Sciences}},
series = {{Mathematics of Operations Research}},
title = {{Equilibria and Systemic Risk in Saturated Networks}},
url = {{http://dx.doi.org/10.1287/moor.2021.1188}},
doi = {{10.1287/moor.2021.1188}},
volume = {{47}},
year = {{2022}},
}