Self-organizing Complex Networks: individual versus global rules

Physical Review E, 2008

This paper aims at understanding coevolutionary dynamics of cooperative behaviors and network structures of interactions. We constructed an evolutionary model in which each individual not only has a strategy for Prisoner's Dilemma (PD) to play with its neighboring members on the network, but also has a strategy for changing its neighboring structure of the network. By conducting evolutionary experiments with various settings of the payoff matrix, we found that the coevolutionary cycles of cooperative behaviors of individuals and their network structures repeatedly occurred when both the temptation to defect and the cost for playing a game were moderate.

2016

Complex networks are a recent type of frameworks used to study complex systems with many interacting elements, such as Self-Organized Criticality (SOC). The network node's tendency to link to other nodes of similar type is characterized by assortative mixing. Real networks exhibit assortative mixing by vertex degree, however typical random network models, such as Erdos-Renyi or Barabasi-Albert, show no assortative arrangements. In this paper we introduce the neighborhood assortativity notion, as the tendency of a node to belong to a community (its neighborhood) showing an average property similar to its own. Imposing neighborhood assortative mixing by degree in a network toy model, SOC dynamics can be found. The long-range correlations resulting from the criticality have been characterized by means of fluctuation analysis and show an anticorrelation in the node's activity. The model contains only one parameter and its statistics plots for different values of the parameter ca...

2001

This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed by a rapid process of local imitation (``diffusion''). Our main focus is on the regularities displayed by the long-run distribution of diffusion waves and their implication on the performance of the system. By integrating analytical techniques and numerical simulations, we come to the following two main conclusions. (1) If dis-coordination costs are sufficiently high, the system behaves critically, in the sense customarily used in physics. (2) The performance of the system is optimal at the frontier of the critical region. Heuristically, this may be interpreted as an indication that (performance-sensitive) evolutionary forces induce the system to be placed ``at the edge of order and chaos''

Understanding Complex Systems, 2009

It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network topology based on a local coupling between a dynamical order parameter and rewiring of network connectivity, with convergence towards criticality in the limit of large network size N. In particular, two adaptive schemes are discussed and compared in the context of Boolean Networks and Threshold Networks: 1) Active nodes loose links, frozen nodes aquire new links, 2) Nodes with correlated activity connect, de-correlated nodes disconnect. These simple local adaptive rules lead to co-evolution of network topology and-dynamics. Adaptive networks are strikingly different from random networks: They evolve inhomogeneous topologies and broad plateaus of homeostatic regulation, dynamical activity exhibits 1/ f noise and attractor periods obey a scale-free distribution. The proposed co-evolutionary mechanism of topological self-organization is robust against noise and does not depend on the details of dynamical transition rules. Using finite-size scaling, it is shown that networks converge to a self-organized critical state in the thermodynamic limit. Finally, we discuss open questions and directions for future research, and outline possible applications of these models to adaptive systems in diverse areas.

Physica A: Statistical Mechanics and its Applications, 2012

Understanding how cooperative behaviour evolves in network communities, where the individual members interact via social dilemma games, is an on-going challenge. In this paper, we introduce a social network based model to investigate the evolution of cooperation in the N-player Prisoner's Dilemma game. As such, this work complements previous studies focused on multi-player social dilemma games and endogenous networks. Agents in our model, employ different game-playing strategies reflecting varying cognitive capacities. When an agent plays cooperatively, a social link is formed with each of the other N − 1 group members. Subsequent cooperative actions reinforce this link. However, when an agent defects, the links in the social network are broken. Computational simulations across a range of parameter settings are used to examine different scenarios: varying population and group sizes; the group formation process (or partner selection); and agent decision-making strategies under varying dilemma constraints (cost-to-benefit ratios), including a ''discriminator'' strategy where the action is based on a function of the weighted links within an agent's social network. The simulation results show that the proposed social network model is able to evolve and maintain cooperation. As expected, as the value of N increases the equilibrium proportion of cooperators in the population decreases. In addition, this outcome is dependent on the dilemma constraint (cost-tobenefit ratio). However, in some circumstances the dynamic social network plays an increasingly important role in promoting and sustaining cooperation, especially when the agents adopt the discriminator strategy. The adjustment of social links results in the formation of communities of ''like-minded'' agents. Subsequently, this local optimal behaviour promotes the evolution of cooperative behaviour at the system level.

Understanding Complex Systems, 2009

Social networks are dynamic: We make new friends and loose touch with old ones, depending on the interactions with them. Most analytic studies of social networks assume that links remain unchanged at all times. In this case, individuals have no control over the number, frequency or duration of their interactions with others. Here, we discuss analytical and numerical models in which individuals can break links and create new ones. Interactions are modeled as general symmetric twoplayer games. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. In the limiting cases where linking dynamics is much faster than evolutionary dynamics or vice-versa, the system can be tackled analytically. We show how the individual capacity of forming new links or severing inconvenient ones can change the nature of the game. If the linking rules are local, numerical simulations show that networks emerge that have several features of real-world social networks.

The Journal of Mathematical Sociology, 2012

In this paper, we critically study whether social networks can explain the emergence of cooperative behavior. We carry out an extensive simulation program in which we study the most representative social dilemmas. For the Prisoner's Dilemma, it turns out that the emergence of cooperation is very dependent on the micro-dynamics. On the other hand, network clustering mostly facilitates global cooperation in the Stag Hunt game, whereas degree heterogeneity promotes cooperation in Snowdrift dilemmas. Thus, social networks do not promote cooperation in general, because the macrooutcome is not robust under change of dynamics. Therefore, having specific applications of interest in mind is crucial to include the appropriate microdetails in a good model.

Computers & Chemical Engineering, 2004

An important feature of many complex systems, both natural and artificial, is the structure and organization of their interaction networks with interesting properties. Here we present a theory of self-organization by evolutionary adaptation in which we show how the structure and organization of a network is related to the survival, or in general the performance, objectives of the system. We propose that a complex system optimizes its network structure in order to maximize its overall survival fitness which is composed of short-term and long-term survival components. These in turn depend on three critical measures of the network, namely, efficiency, robustness and cost, and the environmental selection pressure. Using a graph theoretical case study, we show that when efficiency is paramount the "Star" topology emerges and when robustness is important the "Circle" topology is found. When efficiency and robustness requirements are both important to varying degrees, other classes of networks such as the "Hub" emerge. Our assumptions and results are consistent with observations across a wide variety of applications.