Equilibria and Systemic Risk in Saturated Networks

Leonardo Massai (), Giacomo Como () and Fabio Fagnani ()
Additional contact information
Leonardo Massai: Dipartimento di Scienze Matematiche, Politecnico di Torino, 10129 Torino, Italy
Giacomo Como: Dipartimento di Scienze Matematiche, Politecnico di Torino, 10129 Torino, Italy; Department of Automatic Control, Lund University, SE-22100 Lund, Sweden
Fabio Fagnani: Dipartimento di Scienze Matematiche, Politecnico di Torino, 10129 Torino, Italy

Mathematics of Operations Research, 2022, vol. 47, issue 3, 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. 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.

Keywords: Primary: 91A43; 91A06; 91B05; secondary: 91A43; 91B55; network equilibrium; systemic risk; linear saturated models; financial networks (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2021.1188 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:3:p:1781-1801

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().