Matteo Marsili

Theory of rumour spreading in complex social networks

We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.

Nonequilibrium phase transition in a model for social influence.

We present extensive numerical simulations of the Axelrods model for social influence, aimed at understanding the formation of cultural domains. This is a nonequilibrium model with short range interactions and a remarkably rich dynamical behavior. We study the phase diagram of the model and uncover a nonequilibrium phase transition separating an ordered (culturally polarized) phase from a disordered (culturally fragmented) one. The nature of the phase transition can be continuous or discontinuous depending on the model parameters. At the transition, the size of cultural regions is power-law distributed.

A Prototype Model of Stock Exchange

A prototype model of stock market is introduced and studied numerically. In this self-organized system, we consider only the interaction among traders without external influences. Agents trade according to their own strategy, to accumulate their assets by speculating on the prices fluctuations which are produced by themselves. The model reproduced rather realistic price histories whose statistical properties are also similar to those observed in real markets.

Statistical Mechanics of systems with heterogeneous agents:Minority Games

We study analytically a simple game theoretical model of heterogeneous interacting agents. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes her own utility. The latter turns out to be characterized by a replica symmetry broken structure. Numerical results fully agree with our analytical findings.

Modeling Market Mechanism with Minority Game

Using the minority game model we study a broad spectrum of problems of market mechanism. We study the role of different types of agents: producers, speculators as well as noise traders. The central issue here is the information flow: producers feed in the information whereas speculators make it away. How well each agent fares in the common game depends on the market conditions, as well as their sophistication. Sometimes there is much to gain with little effort, sometimes great effort virtually brings no more incremental gain. Market impact is also shown to play an important role, a strategy should be judged when it is actually used in play for its quality. Though the minority game is an extremely simplified market model, it allows to ask, analyze and answer many questions which arise in real markets.

INTERACTING INDIVIDUALS LEADING TO ZIPF'S LAW

Institut de Physique Th´eorique, Universit´e de Fribourg, CH-1700(February 1, 2008)We present a general approach to explain the Zipf’s law of city distribution. If the simplestinteraction (pairwise) is assumed, individuals tend to form cities in agreement with the well-knownstatisticsPACS numbers: 89.50.+r, 05.20.-y, 05.40.+j

Assessing the relevance of node features for network structure

Networks describe a variety of interacting complex systems in social science, biology, and information technology. Usually the nodes of real networks are identified not only by their connections but also by some other characteristics. Examples of characteristics of nodes can be age, gender, or nationality of a person in a social network, the abundance of proteins in the cell taking part in protein-interaction networks, or the geographical position of airports that are connected by directed flights. Integrating the information on the connections of each node with the information about its characteristics is crucial to discriminating between the essential and negligible characteristics of nodes for the structure of the network. In this paper we propose a general indicator Θ, based on entropy measures, to quantify the dependence of a networks structure on a given set of features. We apply this method to social networks of friendships in U.S. schools, to the protein-interaction network of Saccharomyces cerevisiae and to the U.S. airport network, showing that the proposed measure provides information that complements other known measures.

From Minority Games to Real Markets

We address the question of market efficiency using the Minority Game (MG) model. First we show that removing unrealistic features of the MG leads to models which reproduce a scaling behaviour close to what is observed in real markets. In particular we find that (i) fat tails and clustered volatility arise at the phase transition point and that (ii) the crossover to random walk behaviour of prices is a finite-size effect. This, on one hand, suggests that markets operate close to criticality, where the market is marginally efficient. On the other it allows one to measure the distance from criticality of real markets, using cross-over times. The artificial market described by the MG is then studied as an ecosystem with different species of traders. This clarifies the nature of the interaction and the particular role played by the various populations.

Scaling in currency exchange

We study the scaling behavior in currency exchange rates. Our results suggest that they satisfy scaling with an exponent close to 0.5, but that it differs qualitatively from that of a simple random walk. Indeed price variations cannot be considered as independent variables and subtle correlations are present. Furthermore, we introduce a novel statistical analysis for economic data which makes the physical properties of a signal more evident and eliminates the systematic effects of time periodicity.

Rollover risk, network structure and systemic financial crises

The breakdown of short-term funding markets was a key feature of the global financial crisis of 2007/2008. Drawing on ideas from global games and network growth, we show how network topology interacts with the funding structure of financial institutions to determine system-wide crises. Bad news about a financial institution can lead others to lose confidence in it and their withdrawals, in turn, trigger problems across the interbank network. Once broken, credit relations take a long time to re-establish as a result of common knowledge of the equilibrium. Our findings shed light on public policy responses during and after the crisis.