Self-organizing Complex Networks: individual versus global rules

Abstract

We introduce a form of Self-Organized Criticality (SOC) inspired by the new generation of evolutionary game theory, which ranges from physiology to sociology. The single individuals are the nodes of a composite network, equivalent to two interacting subnetworks, one leading to strategy choices made by the individuals under the influence of the choices of their nearest neighbors and the other measuring the Prisoner's Dilemma Game payoffs of these choices. The interaction between the two networks is established by making the imitation strength K increase or decrease according to whether the last two payoffs increase or decrease upon increasing or decreasing K. Although each of these imitation strengths is selected selfishly, and independently of the others as well, the social system spontaneously evolves toward the state of cooperation. Criticality is signaled by temporal complexity, namely the occurrence of non-Poisson renewal events, the time intervals between two consecutive crucial events being given by an inverse power law index μ = 1.3 rather than by avalanches with an inverse power law distribution as in the original form of SOC. This new phenomenon is herein labeled self-organized temporal criticality (SOTC). We compare this bottom-up self-organization process to the adoption of a global choice rule based on assigning to all the units the same value K, with the time evolution of common K being determined by consciousness of the social benefit, a top-down process implying the action of a leader. In this case self-organization is impeded by large intensity fluctuations and the global social benefit turns out to be much weaker. We conclude that the SOTC model fits the requests of a manifesto recently proposed by a number of European social scientists.

Self‐Organized Temporal Criticality: Bottom‐Up Resilience versus Top‐Down Vulnerability

“…In the case of SOTC [3], with = , see Section 2, we find ] = 0.5. These criticalityinduced fluctuations, becoming visible for finite values of , are referred to as an expression of temporal complexity.…”

“…The model of [3] is a form of spontaneous transition to criticality, revealed by the emergence of events with the temporal properties of crucial events, thereby explaining the adoption of the name Self-Organized Temporal Criticality (SOTC) to define it. We show that the bottom-up SOTC modeling is resilient and that the top-down SOTC modeling is not.…”

“…For clarity in Sections 2 and 3 we provide a review of the SOTC model [3], while stressing some properties of SOTC model that were not discussed in the original paper, for instance, the behavior of single units with their frequent regression to the condition of independence of the other units, for the bottom-up process and the Pareto cycles of the top-down version of the model. The original results of this earlier paper indicated a lack of resilience of the top-down SOTC model and a robustness of the bottom-up SOTC model, which are illustrated in Section 4.…”

“…These important sociological issues were addressed in 1901 by Pareto [2], who discussed the capability that elites should develop in order to adapt themselves to changing circumstances. The main goal of the present paper is to contribute to the discussion on the resilience issue, with a simplified model that was recently proposed by our group to resolve the altruism paradox, namely, the emergence of cooperation from the social interaction of individuals who make their choice between cooperation, , and defection, , on the basis of their self-interest [3].…”

“…The new model of spontaneous organization [3] is based on the conjecture that there are close connections between resilience and information transport, resilience and consciousness, and between consciousness and criticality.…”