Self-organized evolution in a socioeconomic environment

Phase transitions in paradigm shift models

Two general models for paradigm shifts, deterministic propagation model (DM) and stochastic propagation model (SM), are proposed to describe paradigm shifts and the adoption of new technological levels. By defining the order parameter based on the diversity of ideas, , it is studied when and how the phase transition or the disappearance of a dominant paradigm occurs as a cost in DM or an innovation probability in SM increases. In addition, we also investigate how the propagation processes affect the transition nature. From analytical calculations and numerical simulations is shown to satisfy the scaling relation for DM with the number of agents . In contrast, in SM scales as .

Competition of information channels in the spreading of innovations

We study the spreading of information on technological developments in socioeconomic systems where the social contacts of agents are represented by a network of connections. In the model, agents get informed about the existence and advantages of new innovations through advertising activities of producers, which are then followed by an interagent information transfer. Computer simulations revealed that varying the strength of external driving and of interagent coupling, furthermore, the topology of social contacts, the model presents a complex behavior with interesting novel features: On the macrolevel the system exhibits logistic behavior typical for the diffusion of innovations. The time evolution can be described analytically by an integral equation that captures the nucleation and growth of clusters of informed agents. On the microlevel, small clusters are found to be compact with a crossover to fractal structures with increasing size. The distribution of cluster sizes has a power-law behavior with a crossover to a higher exponent when long-range social contacts are present in the system. Based on computer simulations we construct an approximate phase diagram of the model on a regular square lattice of agents.

Morphology of technological levels in an innovation propagation model

We study the dynamical properties of the propagation of innovation on a two-dimensional lattice, random network, scale-free network, and Cayley tree. In order to investigate the diversity of technological level, we study the scaling property of width, W(N,t), which represents the root mean square of the technological level of agents. Here, N is the total number of agents. From the numerical simulations, we find that the steady-state value of W(N,t), W(sat)(N), scales as W(sat)(N) ∼ N(-1/2) when the system is in a flat ordered phase for d ≥ 2. In the flat ordered phase, most of the agents have the same technological level. On the other hand, when the system is in a smooth disordered phase, the value of W(sat)(N) does not depend on N. These behaviors are completely different from those observed on a one-dimensional (1D) lattice. By considering the effect of the underlying topology on the propagation dynamics for d ≥ 2, we also provide a mean-field analysis for W(sat)(N), which agrees very well with the observed behaviors of W(sat)(N). This directly shows that the morphological properties in order-disorder transition on a 1D lattice is completely different from that on higher dimensions. It also provides an evidence that the upper critical dimension for the roughening transition of the propagation of innovation is d(u)=2.

Efficient target strategies for contagion in scale-free networks

Organizations or individuals often have an incentive to target a certain number of agents to launch a contagion process effectively and efficiently, for example, sampling consumers in the diffusion of new products. We present an effective strategy for contagion in scale-free networks. The proposed strategy, hub strategy, calls for targeting mostly the highly connected nodes. The biased level implemented in this strategy characterizes its ability to identify hub nodes. We demonstrate that hub strategy can improve the contagion effects evidently. We find that biased level increases first with heterogeneity level of contagion network but decreases with that after a certain value, and decreases with initial adopter rate all the time. Moreover, degree correlations in contagion networks may reduce biased level.

Nonequilibrium phase transition in a model for the propagation of innovations among economic agents

We characterize the different morphological phases that occur in a simple one-dimensional model of propagation of innovations among economic agents [X. Guardiola et al., Phys. Rev E 66, 026121 (2002)]. We show that the model can be regarded as a nonequilibrium surface growth model. This allows us to demonstrate the presence of a continuous roughening transition between a flat (system size independent fluctuations) and a rough phase (system size dependent fluctuations). Finite-size scaling studies at the transition strongly suggest that the dynamic critical transition does not belong to directed percolation and, in fact, critical exponents do not seem to fit in any of the known universality classes of nonequilibrium phase transitions. Finally, we present an explanation for the occurrence of the roughening transition and argue that avalanche driven dynamics is responsible for the novel critical behavior.

Modeling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.