We provide the probability distribution function of matrix elements each of which is the inner product of two vectors. The vectors we are considering here are independently distributed but not necessarily Gaussian variables. Let M be the number of components of each of the N vectors, one has an...

In this paper, we introduce a modified collaborative filtering (MCF) algorithm, which has remarkably higher accuracy than the standard collaborative filtering. In the MCF, instead of the cosine similarity index, the user–user correlations are obtained by a diffusion process. Furthermore, by...

We analyze different ways of pairing agents in a bipartite matching problem, with regard to its scaling properties and to the distribution of individual “satisfactions”. Then we explore the role of partial information and bounded rationality in a generalized Marriage Problem, comparing the...

We develop a probabilistic consumer choice framework based on information asymmetry between consumers and firms. This framework makes it possible to study market competition of several firms by both quality and price of their products. We find Nash market equilibria and other optimal strategies...

We consider standard percolation processes such as epidemic processes with or without immunization. We show that their dynamics can be formulated so that they mimic self-organized critical phenomena: the wetting probability p needs not to be fine tuned to its critical value pc in order to arrive...

We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are “weakly” stable: irrationality propagates and amplifies through players' interactions so that huge fluctuations can result from a...

The impact of monetary policy changes on the monetary market and stock market in China is investigated in this study. The changes of two major monetary policies, the interest rate and required reserve ratio, are analyzed in a study period covering seven years on the interbank monetary market and...

We propose a continuum model for the description of buyer and seller dynamics in an Internet market. The relevant variables are the research effort of buyers and the sellers’ reputation building process. We show that, if a commercial website gives consumers the possibility to rate credibly...

We propose and study a simple model of dynamical redistribution of capital in a diversified portfolio. We consider a hypothetical situation of a portfolio composed of N uncorrelated stocks. Each stock price follows a multiplicative random walk with identical drift and dispersion. The rules of...

Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game [J.L. Kelly, IEEE Transactions...