TY - JOUR

T1 - Systemic-Risk and Evolutionary Stable Strategies in a Financial Network

AU - Saha, Indrajit

AU - Kavitha, Veeraruna

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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U2 - 10.1007/s13235-022-00488-2

DO - 10.1007/s13235-022-00488-2

M3 - Article

AN - SCOPUS:85146247710

SN - 2153-0785

JO - Dynamic Games and Applications

JF - Dynamic Games and Applications

ER -