Self-Organized Critical Evolution In Economic Systems That Display Local Complementarities

We propose a general scenario to analyze technological changes in socio-economic environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time, sufficiently complex to display a rich dynamic behavior. Our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical, in the sense that the distribution of events follow power-laws. Computer simulations show that, in addition, the system always self-organizes to achieve the optimal performance in the stationary state. There are clear evidences that social and economic change in modern societies typically come in ``waves'' with seemingly little intertemporal structure. There are many factors that can contribute to such complex evolution but, in essence, any theory able to account for the inherent dynamics of the phenomenon should consider how the stimulus for change spreads by gradual local interaction through a social network as well as the incentives that govern individual behavior. The hope is that, independently of the particular choice for the microscopic rules describing the dynamic behavior of the agents that form an arbitrary system, one should observe some collective trends that could be reflected in terms of macroscopic observables.In this work, our main goal is to define a general scenario that could be useful to understand evolution in socio-economic environments and within such a broad field our concern is related to technological progress. In a general sense, let us consider a population of agents each of them interacting with a group of neighbors in order to carry out projects of mutual interest. From these collaborations agents obtain payoffs which, of course, tend individually to be as large as possible. To be more precise these payoffs should reflect several basic properties. First, they should account for a basic benefit obtained just for having a certain technological level. It might be thought as an index for the technological potential productivity. It is reasonable to assume that the higher the technological level the larger the base payoff will be. Furthermore, it should measure how similar the tools required to undertake a mutual project are. It should favor those collaborations where both technological levels are very similar (high compatibility) and punish any waste of resources derived from a possible mismatch between them. In other words, technological compatibility should induce high values of the payoff function while significant costs should arise from any degree of incompatibility. It is also reasonable to assume that those costs are bounded from below (the bankrupt).The dynamics must be consequent with the aforementioned basic trends. Two main ingredients contribute to the dynamical evolution. One is the interaction with the rest of the population. Each agent should have the possibility to modify her technological level if the benefits derived from this change are increased. With only this term the system might reach a quiescent state where all the agents are happy with their respective technological level, not necessarily the same for all of them. To complete the picture, it is also natural to think of individual mechanisms of technological improvement which could be modeled as a sudden update of the state of a given agent. This change plays the role of a perturbation and admits several interpretations (e.g. local innovation, a shock in payoffs, population renewal, etc.). Immediately, her nearest neighbors check whether an update to a new technological state is more profitable for them. The process can be extended all over the network triggering a wave of change or avalanche till a new quiescent state is reached. Then, the sequence of events is repeated again. Notice that in modern socio-economic environments, the diffusion of information/technology is usually a fast process while advances are developed in a much slower time scale. Therefore, it is reasonable to assume that both processes are defined in different time scales. Other ingredients can also be incorporated into this general framework but, up to now, let us keep this simple picture in mind.We present here a general scenario for the study of the technological evolution in a socio-economic environment. It is quite appealing to realize that in a very general manner the framework described in this paper is able to predict the existence of different regimes depending on the cost associated to the improvement/diffussion of technology and that these regimes can be computed directly from a macroscopic quantity without specifying details about the underlying microscopic dynamics and payoff functions. Even more, we have shown through a simple model that critical behavior is attained in a natural way through a process of self-organization that maximizes a macroscopic observable: the advance rate.