Abstract. This paper introduces a Markov chain approach that allows a rigorous analysis of agent based opinion dynamics as well as other related agent based models (ABM). By viewing the ABM dynamics as a micro description of the process, we show how the corresponding macro description is obtained by a projection construction. Then, well known conditions for lumpability make it possible to establish the cases where the macro model is still Markov. In this case we obtain a complete picture of the dynamics including the transient stage, the most interesting phase in applications. For such a purpose a crucial role is played by the type of probability distribution used to implement the stochastic part of the model which defines the updating rule and governs the dynamics. In addition, we show how restrictions in communication leading to the co-existence of different opinions follow from the emergence of new absorbing states. We describe our analysis in detail with some specific models of opinion dynamics. Generalizations concerning different opinion representations as well as opinion models with other interaction mechanisms are also discussed. We find that our method may be an attractive alternative to mean-field approaches and that this approach provides new perspectives on the modeling of opinion exchange dynamics, and more generally of other ABM.
This paper investigates the dynamics of stocks in the S&P 500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose that is a robust index of the dynamics of the market structure and provides information on the intensity and the sectoral impact of crises. With this measure, we analyse the effects of extreme phenomena on the geometry of the market. Nine crashes between 1987 and 2001 are compared by looking at the way they modify the shape of the manifold that describes the S&P 500 market space.Agent-based modelling, Applied finance, Artificial economy, Complexity in economics, Complexity in finance, Computational finance, Economic modelling, Evolutionary model of currency crisis,
This paper examines the interplay of opinion exchange dynamics and communication network formation. An opinion formation procedure is introduced which is based on an abstract representation of opinions as k-dimensional bit-strings. Individuals interact if the difference in the opinion strings is below a defined similarity threshold dI . Depending on dI , different behaviour of the population is observed: low values result in a state of highly fragmented opinions and higher values yield consensus. The first contribution of this research is to identify the values of parameters dI and k, such that the transition between fragmented opinions and homogeneity takes place. Then, we look at this transition from two perspectives: first by studying the group size distribution and second by analysing the communication network that is formed by the interactions that take place during the simulation. The emerging networks are classified by statistical means and we find that non-trivial social structures emerge from simple rules for individual communication. Generating networks allows to compare model outcomes with real-world communication patterns.Such an abstract bit-string approach has been used in the simulation of consumer-producer behaviour [6] as well as in the context of labour market analysis [5] where bit-strings represent products (or job offers) and needs (worker skills). Here, each bit-string represents an agent opinion and a procedure of agent-agent interaction is specified based on assumptions from social comparison theory [15] and in opinion formation models [7,12,3,26,27].This paper is organized in the following way. We start reviewing previous approaches to the modelling of opinion exchange dynamics. After this, we give an explanation of our model. This is followed by a numerical analysis, in which the opinion evolution is considered before looking at the emerging networks of communication activity. A discussion of the results concludes this work.1 Behaviour classes refer to qualitative different behaviours that potentially result from a simulation model.
Gender differences in collaborative research have received little attention when compared with the growing importance that women hold in academia and research. Unsurprisingly, most of bibliometric databases have a strong lack of directly available information by gender. Although empirical-based network approaches are often used in the study of research collaboration, the studies about the influence of gender dissimilarities on the resulting topological outcomes are still scarce. Here, networks of scientific subjects are used to characterize patterns that might be associated to five categories of authorships which were built based on gender. We find enough evidence that gender imbalance in scientific authorships brings a peculiar trait to the networks induced from papers published in Web of Science (WoS) indexed journals of Economics over the period 2010-2015 and having at least one author affiliated to a Portuguese institution. Our results show the emergence of a specific pattern when the network of co-occurring subjects is induced from a set of papers exclusively authored by men. Such a male-exclusive authorship condition is found to be the solely responsible for the emergence that particular shape in the network structure. This peculiar trait might facilitate future network analyses of research collaboration and interdisciplinarity.
The recent financial crisis has stressed the need to understand financial systems as networks of interdependent countries, where crossborder financial linkages play the fundamental role. It has also been emphasized that the relevance of these networks relies on the representation of changes follow-on the occurrence of stress events. Here, from series of interbank liabilities and claims over different time periods, we have developed networks of positions (net claims) between countries. Besides the Minimal Spanning Tree analysis of the time-constrained networks, a coefficient of residuality is defined to capture the structural evolution of the network of cross-border financial linkages. Because some structural changes seem to be related to the role that countries play in the financial context, networks of debtor and creditor countries are also developed. Empirical results allows to relate the network structure that emerges in the last years to the globally turbulent period that has characterized financial systems since the latest nineties. The residuality coefficient highlights an important modification acting in the financial linkages across countries in the period 1997-2011, and situates the recent financial crises as replica of a larger structural change going on since 1997.
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