Financial Replicator Dynamics: Emergence of Systemic-Risk-Averting Strategies

We consider a random financial network with large number of agents. The agents connect through credit instruments borrowed from each other or direct lending, and these create the liabilities. settlement debts various at end contract period can be expressed as solutions fixed point equations. Our first step is to derive (asymptotically), using recent result on population in which adapt one two available strategies, risky risk-free investments, an aim maximize their expected returns (or surplus). study emerging strategies when different types replicator dynamics capture inter-agent interactions. theoretically reduced analysis complex system that appropriate ordinary differential equation (ODE). proved equilibrium converge almost surely attractor ODE. also derived conditions under mixed evolutionary stable strategy (ESS) emerges; scenarios converges both populations are equal. Further average (choices based observation sample) always averts systemic risk events (events fraction defaults). verified Monte Carlo simulations suggested by ODE method indeed represents limit dynamics.