This book is a course in methods and models rooted in physics and used in modelling economic and social phenomena. It covers the discipline of econophysics, which creates an interface between physics and economics. Besides the main theme, it touches on the theory of complex networks and...

The network of users in the Internet auction site Aukro.cz is analyzed. We show that the fluctuations in the activity of users has non-Gaussian distribution with long-time correlations. The bipartite network of auctions and users has degree distribution following a stretched exponential. The...

We analyze empirical data from the internet auction site Aukro.cz. The time series of activity shows truncated fractal structure on scales from about 1 min to about 1 day. The distribution of waiting times as well as the distribution of number of auctions within fixed interval is a power law,...

We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool here is localization of eigenvectors of the matrix, by...

A model of open economics composed of producers and speculators is investigated by numerical simulations. The capital flows from the environment to the producers and from them to the speculators. The price fluctuations are suppressed by the speculators. When the aggressivity of the speculators...

We introduce a new kind of Information Theory. From a finite number of local, noisy comparisons, we want to design a robust filter such that the outcome is a high ranking number. Both analytical and numerical results are encouraging and we believe our toy model has wide ranging implications in...

We analyze the theory of optimal investment in risky assets, developed recently by Marsili et al. (Physica A 253 (1998) 403). When the real data are used instead of abstract stochastic process, it appears that a non-trivial investment strategy is rarely possible. We show that non-zero...

We study the role of imitation within a model of economics with adaptive agents. The basic ingredients are those of the minority game. We add the possibility of local information exchange and imitation of the neighbour's strategy. Imitators should pay a fee to the imitated. Connected groups are...

We systematically compare several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can...