Learning Sparse Polymatrix Games in Polynomial Time and Sample Complexity

We consider the problem of learning sparse polymatrix games from observations of strategic interactions. We show that a polynomial time method based on $\ell_{1,2}$-group regularized logistic regression recovers a game, whose Nash equilibria are the $\epsilon$-Nash equilibria of the game from which the data was generated (true game), in $\mathcal{O}(m^4 d^4 \log (pd))$ samples of strategy profiles --- where $m$ is the maximum number of pure strategies of a player, $p$ is the number of players, and $d$ is the maximum degree of the game graph. Under slightly more stringent separability conditions on the payoff matrices of the true game, we show that our method learns a game with the exact same Nash equilibria as the true game. We also show that $\Omega(d \log (pm))$ samples are necessary for any method to consistently recover a game, with the same Nash-equilibria as the true game, from observations of strategic interactions. We verify our theoretical results through simulation experiments

A LONGITUDINAL STATISTICAL NETWORK ANALYSIS OF THE ENVIRONMENTAL ITIGATION AND ALLIANCES IN THE UNITED STATES, 1970-2001

This dissertation investigates the structural dynamics of the inter-organizational (litigation, alliance) relations in the environmental movement sector (EMS) in the United States, 1970-2001. Particularly, it focuses on the litigative and alliance ties between the environmental organizations (EORGs) including both environmental movement organizations (EMOs) and environmental government agencies (EGAs), and explaining the processes by which the contemporary inter-EORG structure has emerged over time. The methods used in analysis include (balance, structural) partitioning, p-star logit, and categorical data analysis in statistical network analysis. The data analyzed were collected from various sources including LexisNexis and Guide Star and include both organizational attributes and relations. To explicate the dynamic processes by which the contemporary inter-EORG structure has emerged, this dissertation investigates the formation of dyadic, triadic, and network structure with regard to litigative and alliance ties, respectively. Selected fundamental models of network dynamics (transitive dominance, strategic actor, and social balance) help explain the empirical inter-organizational (litigation, alliance) relations in later chapters. The theoretical and empirical findings help better understand the structural and dynamic issues in the study of the environment, social movement, complex organizations, and network evolution

Flow of online misinformation during the peak of the COVID-19 pandemic in Italy

The COVID-19 pandemic has impacted on every human activity and, because of the urgency of finding the proper responses to such an unprecedented emergency, it generated a diffused societal debate. The online version of this discussion was not exempted by the presence of d/misinformation campaigns, but differently from what already witnessed in other debates, the COVID-19 -- intentional or not -- flow of false information put at severe risk the public health, reducing the effectiveness of governments' countermeasures. In the present manuscript, we study the effective impact of misinformation in the Italian societal debate on Twitter during the pandemic, focusing on the various discursive communities. In order to extract the discursive communities, we focus on verified users, i.e. accounts whose identity is officially certified by Twitter. We thus infer the various discursive communities based on how verified users are perceived by standard ones: if two verified accounts are considered as similar by non unverified ones, we link them in the network of certified accounts. We first observe that, beside being a mostly scientific subject, the COVID-19 discussion show a clear division in what results to be different political groups. At this point, by using a commonly available fact-checking software (NewsGuard), we assess the reputation of the pieces of news exchanged. We filter the network of retweets (i.e. users re-broadcasting the same elementary piece of information, or tweet) from random noise and check the presence of messages displaying an url. The impact of misinformation posts reaches the 22.1% in the right and center-right wing community and its contribution is even stronger in absolute numbers, due to the activity of this group: 96% of all non reputable urls shared by political groups come from this community.Comment: 25 pages, 4 figures. The Abstract, the Introduction, the Results, the Conclusions and the Methods were substantially rewritten. The plot of the network have been changed, as well as table

COVARIANCE AND CORRELATION ESTIMATORS IN BIPARTITE SYSTEMS

We present a weighted estimator of the covariance and correlation in bipartite complex systems with a double layer of heterogeneity. The advantage provided by the weighted estimators lies in the fact that the unweighted sample covariance and correlation can be shown to possess a bias. Indeed, such a bias affects real bipartite systems, and, for example, we report its effects on two empirical systems, one social and the other biological. On the contrary, our newly proposed weighted estimators remove the bias and are better suited to describe such systems