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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(More)
Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these networks. Here a dynamical approach is used to characterize the small-world phenomenon. Using the β−model, a coupled map(More)
The statistical properties of a stochastic process may be described (1)by the expectation values of the observables, (2)by the probability distribution functions or (3)by probability measures on path space. Here an analysis of level (3) is carried out for market fluctuation processes. Gibbs measures and chains with complete connections are considered. Some(More)
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 ,(More)
A model is developed to study the effectiveness of innovation and its impact on structure creation on agent-based societies. The abstract model that is developed is easily adapted to any particular field. In an interacting environment, the agents receive something from the environment (the other agents) in exchange for their effort and pay the environment a(More)
A model is developed to study the effectiveness of innovation and its impact on structure creation and structure change on agent-based societies. The abstract model that is developed is easily adapted to any particular field. In any interacting environment, the agents receive something from the environment (the other agents) in exchange for their effort and(More)
This paper investigates the dynamics of stocks in the S&P500 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, which is a robust index of the dynamics of the market structure and provides information on the intensity and the sectoral impact of the(More)
We analyze the dynamics of agent–based models (ABMs) from a Markovian perspective and derive explicit statements about the possibility of linking a microscopic agent model to the dynamical processes of macroscopic observables that are useful for a precise understanding of the model dynamics. In this way the dynamics of collective variables may be studied,(More)
Endogenous, ideas-led, growth theory and agent based modelling with neighbourhood effects literature are crossed. In an economic overlapping generations framework, it is shown how social interactions and neighbourhood effects are of vital importance in the endogenous determination of the long run number of skilled workers and therefore of the growth(More)