The Medieval Inquisition: Scale-free Networks and the Suppression of Heresy

Qualitative evidence suggests that heresy within the medieval Catholic Church had many of the characteristics of a scale-free network. From the perspective of the Church, heresy can be seen as a virus. The virus persisted for long periods of time, breaking out again even when the Church believed it to have been eradicated. A principal mechanism of heresy was through a small number of individuals with very large numbers of social contacts. Initial attempts by the Inquisition to suppress the virus by general persecution, or even mass slaughtering, of populations thought to harbour the "disease" failed. Gradually, however, the Inquisition learned about the nature of the social networks by which heresy both spread and persisted. Eventually, a policy of targeting key individuals was implemented, which proved to be much more successful.Comment: 12 page

How much can firms know?

There are two key stylised facts about the extinction patterns of firms. First, the probability of extinction is highest at the start of the firm"s existence, but soon becomes more or less invariant to the age of the firm. Second, the relationship between the size and frequency of firm extinctions is closely approximated by a power law. An agent based model of firm evolution and extinction has been developed which has properties which conform closely to the stylised facts. We examine the effects of allowing firms different amounts of knowledge about the effects of strategy in the context of this agent-based evolutionary model. There are very considerable returns in the model to acquiring knowledge. As both the amount of knowledge available to firms increases and as the number of firms capable of acquiring such knowledge rises, the lifespan of agents approaches the full information paradigm in which agents live for ever. However, even with relatively low levels of knowledge and numbers of agents capable of acquiring it, the model ceases to have properties which are compatible with the two key stylised facts on firm extinctions. The clear implication is that firms have very limited capacities to acquire knowledge about the true impact of their strategies.agent based evolutionary model; heterogenous agents; learning

Cascades of Failure and Extinction in Evolving Complex Systems

There is empirical evidence from a range of disciplines that as the connectivity of a network increases, we observe an increase in the average fitness of the system. But at the same time, there is an increase in the proportion of failure/extinction events which are extremely large. The probability of observing an extreme event remains very low, but it is markedly higher than in the system with lower degrees of connectivity. We are therefore concerned with systems whose properties are not static but which evolve dynamically over time. The focus in this paper, motivated by the empirical examples, is on networks in which the robustness or fragility of the vertices is not given, but which themselves evolve over time We give examples from complex systems such as outages in the US power grid, the robustness properties of cell biology networks, and trade links and the propagation of both currency crises and disease. We consider systems which are populated by agents which are heterogeneous in terms of their fitness for survival. The agents are connected on a network, which evolves over time. In each period agents take self-interested decisions to increase their fitness for survival to form alliances which increase the connectivity of the network. The network is subjected to external negative shocks both with respect to the size of the shock and the spatial impact of the shock. We examine the size/frequency distribution of extinctions and how this distribution evolves as the connectivity of the network grows. The results are robust with respect to the choice of statistical distribution of the shocks. The model is deliberately kept as parsimonious and simple as possible, and refrains from incorporating features such as increasing returns and externalities arising from preferential attachment which might bias the model in the direction of having the empirically observed features of many real world networks. The model still generates results consistent with the empirical evidence: increasing the number of connections causes an increase in the average fitness of agents, yet at the same time makes the system as whole more vulnerable to catastrophic failure/extinction events on an near-global scale.Agent-Based Model; Connectivity; Complex Systems; Networks

Social network markets: the influence of network structure when consumers face decisions over many similar choices

In social network markets, the act of consumer choice in these industries is governed not just by the set of incentives described by conventional consumer demand theory, but by the choices of others in which an individual's payoff is an explicit function of the actions of others. We observe two key empirical features of outcomes in social networked markets. First, a highly right-skewed, non-Gaussian distribution of the number of times competing alternatives are selected at a point in time. Second, there is turnover in the rankings of popularity over time. We show here that such outcomes can arise either when there is no alternative which exhibits inherent superiority in its attributes, or when agents find it very difficult to discern any differences in quality amongst the alternatives which are available so that it is as if no superiority exists. These features appear to obtain, as a reasonable approximation, in many social network markets. We examine the impact of network structure on both the rank-size distribution of choices at a point in time, and on the life spans of the most popular choices. We show that a key influence on outcomes is the extent to which the network follows a hierarchical structure. It is the social network properties of the markets, the meso-level structure, which determine outcomes rather than the objective attributes of the products.Comment: 14 pages, 5 figure