Stefano Battiston

A model of a trust-based recommendation system on a social network

In this paper, we present a model of a trust-based recommendation system on a social network. The idea of the model is that agents use their social network to reach information and their trust relationships to filter it. We investigate how the dynamics of trust among agents affect the performance of the system by comparing it to a frequency-based recommendation system. Furthermore, we identify the impact of network density, preference heterogeneity among agents, and knowledge sparseness to be crucial factors for the performance of the system. The system self-organises in a state with performance near to the optimum; the performance on the global level is an emergent property of the system, achieved without explicit coordination from the local interactions of agents.

The Network of Global Corporate Control

The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.

DebtRank: Too Central to Fail? Financial Networks, the FED and Systemic Risk

Systemic risk, here meant as the risk of default of a large portion of the financial system, depends on the network of financial exposures among institutions. However, there is no widely accepted methodology to determine the systemically important nodes in a network. To fill this gap, we introduce, DebtRank, a novel measure of systemic impact inspired by feedback-centrality. As an application, we analyse a new and unique dataset on the USD 1.2 trillion FED emergency loans program to global financial institutions during 2008–2010. We find that a group of 22 institutions, which received most of the funds, form a strongly connected graph where each of the nodes becomes systemically important at the peak of the crisis. Moreover, a systemic default could have been triggered even by small dispersed shocks. The results suggest that the debate on too-big-to-fail institutions should include the even more serious issue of too-central-to-fail.

Systemic risk in a unifying framework for cascading processes on networks

AbstractWe introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, X*, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of X* as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class leads to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions determine a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.

Web search queries can predict stock market volumes.

We live in a computerized and networked society where many of our actions leave a digital trace and affect other people’s actions. This has lead to the emergence of a new data-driven research field: mathematical methods of computer science, statistical physics and sociometry provide insights on a wide range of disciplines ranging from social science to human mobility. A recent important discovery is that search engine traffic (i.e., the number of requests submitted by users to search engines on the www) can be used to track and, in some cases, to anticipate the dynamics of social phenomena. Successful examples include unemployment levels, car and home sales, and epidemics spreading. Few recent works applied this approach to stock prices and market sentiment. However, it remains unclear if trends in financial markets can be anticipated by the collective wisdom of on-line users on the web. Here we show that daily trading volumes of stocks traded in NASDAQ-100 are correlated with daily volumes of queries related to the same stocks. In particular, query volumes anticipate in many cases peaks of trading by one day or more. Our analysis is carried out on a unique dataset of queries, submitted to an important web search engine, which enable us to investigate also the user behavior. We show that the query volume dynamics emerges from the collective but seemingly uncoordinated activity of many users. These findings contribute to the debate on the identification of early warnings of financial systemic risk, based on the activity of users of the www.

The scale-free topology of market investments

We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree (kin) and the sum of incoming link weights (v) of an investor correspond to the number of assets held (portfolio diversification) and to the invested wealth (portfolio volume), respectively. An empirical analysis of three different real markets reveals that the distributions of both kin and v display power-law tails with exponents γ and α. Moreover, we find that kin scales as a power-law function of v with an exponent β. Remarkably, despite the values of α, β and γ differ across the three markets, they are always governed by the scaling relation β=(1-α)/(1-γ). We show that these empirical findings can be reproduced by a recent model relating the emergence of scale-free networks to an underlying Paretian distribution of ‘hidden’ vertex properties.

Complexity theory and financial regulation

Economic policy needs interdisciplinary network analysis and behavioral modeling Traditional economic theory could not explain, much less predict, the near collapse of the financial system and its long-lasting effects on the global economy. Since the 2008 crisis, there has been increasing interest in using ideas from complexity theory to make sense of economic and financial markets. Concepts, such as tipping points, networks, contagion, feedback, and resilience have entered the financial and regulatory lexicon, but actual use of complexity models and results remains at an early stage. Recent insights and techniques offer potential for better monitoring and management of highly interconnected economic and financial systems and, thus, may help anticipate and manage future crises.

Personalised and dynamic trust in social networks

We propose a novel trust metric for social networks which is suitable for application to recommender systems. It is personalised and dynamic, and allows to compute the indirect trust between two agents which are not neighbours based on the direct trust between agents that are neighbours. In analogy to some personalised versions of PageRank, this metric makes use of the concept of feedback centrality and overcomes some of the limitations of other trust metrics. In particular, it does not neglect cycles and other patterns characterising social networks, as some other algorithms do. In order to apply the metric to recommender systems, we propose a way to make trust dynamic over time. We show by means of analytical approximations and computer simulations that the metric has the desired properties. Finally, we carry out an empirical validation on a dataset crawled from an Internet community and compare the performance of a recommender system using our metric to one using collaborative filtering.

Backbone of complex networks of corporations: the flow of control.

We present a methodology to extract the backbone of complex networks based on the weight and direction of links, as well as on nontopological properties of nodes. We show how the methodology can be applied in general to networks in which mass or energy is flowing along the links. In particular, the procedure enables us to address important questions in economics, namely, how control and wealth are structured and concentrated across national markets. We report on the first cross-country investigation of ownership networks, focusing on the stock markets of 48 countries around the world. On the one hand, our analysis confirms results expected on the basis of the literature on corporate control, namely, that in Anglo-Saxon countries control tends to be dispersed among numerous shareholders. On the other hand, it also reveals that in the same countries, control is found to be highly concentrated at the global level, namely, lying in the hands of very few important shareholders. Interestingly, the exact opposite is observed for European countries. These results have previously not been reported as they are not observable without the kind of network analysis developed here.

The efficiency and stability of R&D networks

We investigate the efficiency and stability of R&D networks in a model with network-dependent indirect spillovers. We show that the efficient network structure critically depends on the marginal cost of R&D collaborations. When the marginal cost is low, the complete graph is efficient, while high marginal costs imply that the efficient network is asymmetric and has a nested structure. Regarding the stability of network structures, we show the existence of both symmetric and asymmetric equilibria. The efficient network is stable for small industry size and small cost. In contrast, for large industry size, there is a wide region of cost in which the efficient network is not stable. This implies a divergence between efficiency and stability in large industries.