Network and Agent Dynamics with Evolving Protection against Systemic Risk

Abstract

The dynamics of protection processes has been a fundamental challenge in systemic risk analysis. The conceptual principle and methodological techniques behind the mechanisms involved (in such dynamics) have been harder to grasp than researchers understood them to be. In this paper, we show how to construct a large variety of behaviors by applying a simple algorithm to networked agents, which could, conceivably, offer a straightforward way out of the complexity. The model starts with the probability that systemic risk spreads. Even in a very random social structure, the propagation of risk is guaranteed by an arbitrary network property of a set of elements. Despite intensive systemic risk, the potential of the absence of failure could also be driven when there has been a strong investment in protection through a heuristically evolved protection level. It is very interesting to discover that many applications are still seeking the mechanisms through which networked individuals build many of these protection processes or mechanisms based on fitness due to evolutionary drift. At the same time, this approach could be useful for researchers and those who need to use protection dynamics to guard against systemic risk under intrinsic randomness in artificial circumstances.

Role of Recovery in Evolving Protection against Systemic Risk: A Mechanical Perspective in Network-Agent Dynamics

“…If A denotes the adjacency matrix of the graph, the eigenvector centrality or x must satisfy the equation Ax � λx, where the vector is normalized to 1. We can normalize this vector to a maximum value, which brings the vector components closer to 1; here, f p1 is important for the measurement of f p (note that we did not explicitly demonstrate this because it has been shown in a previous study [1]). e value for f p must be truncated to the interval (0, 1 − f m ).…”

“…e results imply that contagion and systemic risk are likely to be intensified by the parameter setting (i.e., p p,max , c p,1/2 , and f p ), resulting in a significant failure cost [30]. Note that the failure potential 1 − p p also changes in relation to the choice of strategy values f p0 and f p1 based on social learning (p r ∈ [0, 1]) and exploration (p e ∈ [0, 1]) because these probabilities can lead to different levels of protection in f p [1].…”

“…We propose a modified version of the protection model against systemic risk in terms of its failure recovery mechanics, as demonstrated above. e mechanisms here are based on a few simple basic rules: a node fails at a time with a probability of failure if its failure potential is greater than or equal to that of its nearest neighbors [1], and it fails owing to the interconnected potential, although it spontaneously recovers at an external recovery or according to an intervention probability [3]. e consequences of the damage are crucial for systemic risk and controllability; however, they have not been explored systematically thus far [38].…”

“…Background. Various contemporary studies have argued that systemic risk and abrupt failure events are related to the highly interconnected systems and networked structures created by agents [1]. Based on a simple set of properties, observations derived from several models indicate that the proportion of protection between nodes in the network can be described as a probability.…”

“…Using the same initial parameter values(p p,max � 1, c p,1/2 � 1, p r � 0.1, p e � 0.1, C � 1), this set of the plots represents the time delay case (left-hand side: r_t � 1; right-hand side: r_t � 5). In each section, the plot on the left-hand side shows the matrix (horizontal axis � time step from 1 to 16; vertical axis � individuals from 1 to 16; color of the matrix � failure state: failure [red] and absence of failure [blue]) corresponding to each individual's parameter values at the given time step (t � 16: orange: fp_0 � strategy[1]; cyan: fp_1 � strategy[2]; red: fail � failure; green: pro � protection potential [p p ]). e graph on the right-hand side represents the dynamics in a random regular network, such that the node number � random label for each node and the node color � state (failure � red, absence of failure � blue) (see Appendix 3 for the results of the entire simulation).…”