Narrow Results

A social group is represented by a graph, where each pair of nodes is connected by two oppositely directed links. At the beginning, a given amount p(i) of resources is assigned randomly to each node i. Also, each link r(i,j) is initially represented by a random positive value, which means the percentage of resources of node i which is offered to node j. Initially, the graph is fully connected, i.e., all nondiagonal matrix elements r(i,j) are different from zero. During the simulation, the amounts of resources p(i) change according to the balance equation. The nodes reorganize their activity with time to give more resources to those which give them more. This is the rule of varying the coefficients r(i,j). The result is that after some transient time, only some pairs (m,n) of nodes survive with nonzero p(m) and p(n), each pair with symmetric and positive r(m,n)=r(n,m). Other coefficients r(m,i≠n) vanish. Unpaired nodes remain with no resources, i.e., their p(i)=0, and they cease to be active as they have nothing to offer. The percentage of survivors (i.e., those with p(i) positive) increases with the velocity of varying the numbers r(i,j), and it slightly decreases with the size of the group. The picture and the results can be interpreted as a description of a social algorithm leading to marriages.

A multi-agent spin model for changes of prices in the stock market is considered, based on the Ising-like cellular automaton with global, randomly varying in time interactions between traders. The presence of "fundamentalists" is taken into account by introducing additional term in the local field acting on each agent, dependent on the ratio between the actual stock price and its fundamental value. Numerical multi-agent as well as mean-field simulations show that for properly chosen parameters, the time series of logarithmic price returns exhibit bursting typical of volatility clustering, due to appearance of attractor bubbling in the model. Distributions of price returns show the power-law tails, and the corresponding cumulative distributions have regions of power scaling, with exponents comparable to those observed in empirical time series of stock price returns.

A three-state model based on the Potts model is proposed to simulate financial markets. The three states are assigned to "buy", "sell" and "inactive" states. The model shows the main stylized facts observed in the financial market: fat-tailed distributions of returns and long time correlations in the absolute returns. At low inactivity rate, the model effectively reduces to the two-state model of Bornholdt and shows similar results to the Bornholdt model. As the inactivity increases, we observe the exponential distributions of returns.

The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales. In the present work, we analyze the daily closures of four of the most important indices worldwide since 2000: the DAX for Germany and the NASDAQ-100, the S&P 500 and the Dow Jones for the United States. The qualitative behavior of these different markets is similar during the temporal frame studied. Evidence is found for decelerating log-periodic oscillations of duration about two years and starting in September 2000. Moreover, a nested sub-structure starting in May 2002 is revealed, bringing more evidence to support the hypothesis of self-similar, log-periodic behavior. Ongoing log-periodic oscillations are also revealed. A Lomb analysis over the aforementioned periods indicates a preferential scaling factor λ~2. Higher order harmonics are also present. The spectral pattern of the data has been found to be similar to that of a Weierstrass-type function, used as a prototype of a log-periodic fractal function.

In the present work, we propose a microscopic model of financial markets based on particle-cluster aggregation on a two-dimensional small-world information network in order to simulate the dynamics of the stock markets. "Stylized facts" of the financial market time series, such as fat-tail distribution of returns, volatility clustering and multifractality, are observed in the model. The results of the model agree with empirical data taken from historical records of the daily closures of the NYSE composite index.

The rural-urban migration phenomenon is analyzed by using an agent-based computational model. Agents are placed on lattices which dimensions varying from d =2 up to d =7. The localization of the agents in the lattice defines that their social neighborhood (rural or urban) is not related to their spatial distribution. The effect of the dimension of lattice is studied by analyzing the variation of the main parameters that characterizes the migratory process. The dynamics displays strong effects even for around one million of sites, in higher dimensions (d =6, 7).

Economy correlations between the 19 richest countries are investigated through their Gross Domestic Product increments. A distance is defined between increment correlation matrix elements and their evolution studied as a function of time and time window size. Unidirectional and Bidirectional Minimal Length Paths are generated and analyzed for different time windows. A sort of critical correlation time window is found indicating a transition for best observations. The mean length path decreases with time, indicating stronger correlations. A new method for estimating a realistic minimal time window to observe correlations and deduce macroeconomy conclusions from such features is thus suggested.

Using data from a sample of 28 representatives countries, we propose a classification of currency crises consequences based on the ultrametric analysis of the real exchange rate movements time series, without any further assumption. By using the matrix of synchronous linear correlation coefficients and the appropriate metric distance between pairs of countries, we were able to construct a hierarchical tree of countries. This economic taxonomy provides relevant information regarding liaisons between countries and a meaningful insight about the contagion phenomenon.

Science and technology have a fundamental role in the economic development. Although this statement is generally well accepted, the internal mechanisms which are responsible for these interactions are not clear. In the last decade, dealing with this problem, many models have been proposed. In this paper, we introduce a model that creates an artificial world economy that is a network of countries. Each country has its own national system of innovation and the interactions between countries are given by functions that connect the competitiveness of their prices and their technological capabilities. Starting from different configurations, the artificial world economy self-organizes itself and creates a hierarchies of countries.

We present a linear agent based model on brand competition. Each agent belongs to one of the two brands and interacts with its nearest neighbors. In the process the agent can decide to change to the other brand if the move is beneficial. The numerical simulations show that the systems always condenses into a state when all agents belong to a single brand. We study the condensation times for different parameters of the model and the influence of different mechanisms to avoid condensation, like anti monopoly rules and brand fidelity.

We use econophysics techniques to investigate the characteristics of the distribution of returns from the All Ordinaries Index and from optimal portfolios constructed from individual stocks on the Australian Stock Exchange. We find in general that the tails of the distributions are asymmetric and that the negative tail favours a power-law behaviour while the positive tail is more Gaussian.

We use a modified Cont–Bouchaud model to explore the effectiveness of trading breaks. The modifications include that the trading activity of the market participants depends positively on historical volatility and that the orders of the agents are conditioned on the observed mispricing. Trading breaks, also called circuit breakers, interrupt the trading process when prices are about to exceed a pre-specified limit. We find that trading breaks are a useful instrument to stabilize financial markets. In particular, trading breaks may reduce price volatility and deviations from fundamentals.

The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of strategic variables and reconnection rules. The inherent structure of node agent "brain" is modeled by a recursive neural network with local and global inputs and feedback connections. For specific parametric combination the complex network displays small-world phenomenon combined with scale-free behavior. The identification of a local leader (network hub, agent whose strategies are frequently adapted by its neighbors) is carried out by repeated random walk process through network. The simulations show empirically relevant dynamics of price returns and volatility clustering. The additional emerging aspects of stylized market statistics are Zipfian distributions of fitness.

In the context of an extension of Axelrod's model for social influence, we study the interplay and competition between the cultural drift, represented as random perturbations, and mass media, introduced by means of an external homogeneous field. Unlike previous studies [J. C. González-Avella et al., Phys. Rev. E72, 065102(R) (2005)], the mass media coupling proposed here is capable of affecting the cultural traits of any individual in the society, including those who do not share any features with the external message. A noise-driven transition is found: for large noise rates, both the ordered (culturally polarized) phase and the disordered (culturally fragmented) phase are observed, while, for lower noise rates, the ordered phase prevails. In the former case, the external field is found to induce cultural ordering, a behavior opposite to that reported in previous studies using a different prescription for the mass media interaction. We compare the predictions of this model to statistical data measuring the impact of a mass media vasectomy promotion campaign in Brazil.

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a finite temperature on hypercubic lattices in dimensions up to five. The model includes a "social" local field which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We find no evidence of "blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic fields. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in different scenarios.

A multi-agent spin model for changes of prices in the stock market based on the Ising-like cellular automaton with interactions between traders randomly varying in time is investigated by means of Monte Carlo simulations. The structure of interactions has topology of a small-world network obtained from regular two-dimensional square lattices with various coordination numbers by randomly cutting and rewiring edges. Simulations of the model on regular lattices do not yield time series of logarithmic price returns with statistical properties comparable with the empirical ones. In contrast, in the case of networks with a certain degree of randomness for a wide range of parameters the time series of the logarithmic price returns exhibit intermittent bursting typical of volatility clustering. Also the tails of distributions of returns obey a power scaling law with exponents comparable to those obtained from the empirical data.

We propose a volatility and uncertainty country ranking based on the entropic analysis of the real exchange rate dynamics. We show that this ranking is highly correlated with the volatility in the gross domestic product after events of currency crises. By comparing entropy with variance ranking we demonstrate that entropy measures better volatility effects of crises.

We present a novel optimization method for an Ising like system suspended in a lattice with nonstatic defects. Depending on the size of the experimental probe the system spontaneously defines a defect free lattice where the control function can be optimized using conventional methods as Metropolis heuristics. We illustrate this method in a lattice with variable defects and show how the magnetization of the system depends on the spontaneous definition of the defect-free lattice. This approximation should be useful as a basis for the definition of systems of agents with imperfect coordination.

This paper investigates the topological properties of bank networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of banking variables. Empirical results suggest that the private and foreign banks tend to form clusters within the network. Furthermore, banks with different sizes are also strongly connected and tend to form clusters. These results are robust to the use of different variables to build the network, such as bank profitability, assets, equity, revenue and loans.

An agent-based model was built representing an economic environment in which m brands are competing for a product market. These agents represent companies that interact within a social network in which a certain agent persuades others to update or shift their brands; the brands of the products they are using. Decision rules were established that caused each agent to react according to the economic benefits it would receive; they updated/shifted only if it was beneficial. Each agent can have only one of the m possible brands, and she can interact with its two nearest neighbors and another set of agents which are chosen according to a particular set of rules in the network topology. An absorbing state was always reached in which a single brand monopolized the network (known as condensation). The condensation time varied as a function of model parameters is studied including an analysis of brand competition using different networks.