Systemic-risk and evolutionary stable strategies in a financial network

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, adopt one of the two available strategies, risky or risk-free 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 showed that the replicator dynamics converges to one of the two pure evolutionary stable strategies (all risky or all risk-free agents); one can have mixed limit only when the observations are imperfect. We verified our theoretical findings using exhaustive Monte Carlo simulations. We established that the dynamics avoid the emergence of the systemic-risk regime (where majority default).Comment: 26 pages, 2 figures and 1 table. arXiv admin note: text overlap with arXiv:2003.0088