Systemic-risk and evolutionary stable strategies in a financial network

TL;DR

This paper models a dynamic financial network where agents adapt investment strategies based on observations, showing that the system tends to stabilize in a risk-averse or risk-seeking equilibrium, with implications for systemic risk.

Contribution

It introduces a novel analysis of evolutionary stable strategies in a dynamic, randomly evolving financial network using fixed point equations and replicator dynamics.

Findings

Replicator dynamics converge to pure stable strategies (all risky or all less risky)

Imperfect observations can lead to mixed strategy equilibria

Systemic risk is avoided unless agents blindly adopt risky strategies

Abstract

We consider a financial network represented at any time instance by a random liability graph which evolves over time. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liability edges. These random edges are modified (locally) by the agents over time, as they learn from their experiences and (possibly imperfect) observations. The settlement of the liabilities of various agents at the end of the contract period (at any time instance) can be expressed as solutions of random fixed point equations. Our first step is to derive the solutions of these equations (asymptotically and one for each time instance), using a recent result on random fixed point equations. The agents, at any time instance, adapt one of the two available strategies, risky or less risky investments, with an aim to maximize their returns. We aim to study the emerging strategies of such replicator dynamics that drives the financial network. We theoretically reduce the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). Using the attractors of the resulting ODE we show that the replicator dynamics converges to one of the two pure evolutionary stable strategies (all risky or all less risky agents); one can have mixed limit only when the observations are imperfect. We verify our theoretical findings using exhaustive Monte Carlo simulations. The dynamics avoid the emergence of the systemic-risk regime (where majority default). However, if all the agents blindly adapt risky strategy it can lead to systemic risk regime.