Threshold models of cascades in large-scale networks

The spread of new beliefs, behaviors, and technologies in social and economic networks are often driven by cascading mechanisms. Global behaviors emerge from the interplay between the interconnections structure and the local agents interactions. We focus on the Threshold Model (TM) of cascades that can be interpreted as the best response dynamics in a network game. Each agent is equipped with an individual threshold representing the number of her neighbors who must have adopted a certain action for that to become the agent's best response. We analyze the TM dynamics on large-scale networks with heterogeneous agents. Through a local mean-field approach, we obtain a nonlinear, one-dimensional, recursive equation that approximates the TM's evolution on most of the networks of a given size and distribution of degrees and thresholds. Specifically, we prove that, on all but a fraction of networks with given degree and threshold statistics that is vanishing as the network size grows large, the actual fraction of adopters of a given action in the TM dynamics is arbitrarily close to the output of the aforementioned recursion. Finally, we analyze the dynamic behavior and bifurcations of this recursion and complement the predictions with numerical simulations on real network testbeds

On games with coordinating and anti-coordinating agents

This work studies Nash equilibria for heterogeneous games where both coordinating and anti-coordinating agents coexist. Whilst games with only coordinating or only anti-coordinating agents are potential also in the presence of heterogenities, this is no longer true for games when a mixture of coordinating and anti-coordinating players interact. We provide a complete characterization of the set of Nash equilibria for games with mixed coordinating and anti-coordinating agents with heterogeneous utilities interacting on an all-to-all network.Comment: 8 pages, 7 figure

Life of the Party: Social Networks, Public Attention, and the Importance of Shocks in the Presidential Nomination Process

We examine the effects of shocks on the invisible Presidential primary in the United States. First, we build on existing models using an algorithm simulating social network shocks. Findings show that positive shocks significantly aid the lead candidate’s chances of winning in the invisible primary. Negative shocks, however, are less detrimental to a lead candidate than positive shocks are helpful, as the leader is often able to survive a negative shock and still emerge victorious. Broad empirical tests demonstrate the importance of shocks as well. Beyond the importance of shocks, findings also suggest that Presidential candidate success in the invisible primary owes more to public- than elite-driven factors

Cascading failures: dynamics, stability and control

We develop a dynamic model of cascading failures in a financial network whereby cross-holdings are viewed as feedback, external assets investments as inputs and failure penalties as static nonlinearities. We provide sufficient milder and stronger conditions for the system to be a positive one, and study equilibrium points and stability. Stability implies absence of cascades and convergence of market values to constant values. We provide a constructive method for control design to obtain stabilizing market investments in the form of feedback-feedforward control inputs

Equilibria and Systemic Risk in Saturated Networks

We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations and is one of the simplest continuous models accounting for shock propagation phenomena and cascading failure effects. It also characterizes Nash equilibria of constrained quadratic network games with strategic complementarities. We first derive explicit expressions for network equilibria and prove necessary and sufficient conditions for their uniqueness encompassing and generalizing results available in the literature. Then, we study jump discontinuities of the network equilibria when the exogenous flows cross certain regions of measure 0 representable as graphs of continuous functions. Finally, we discuss some implications of our results in the two main motivating applications. In financial networks, this bifurcation phenomenon is responsible for how small shocks in the assets of a few nodes can trigger major aggregate losses to the system and cause the default of several agents. In constrained quadratic network games, it induces a blow-up behavior of the sensitivity of Nash equilibria with respect to the individual benefits.Comment: 26 page

Optimal Targeting in Super-Modular Games

We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these players are forced to a controlled value while the others are left to repeatedly play a best response action, the system will converge to the greatest Nash equilibrium of the game. Our main contributions consist in showing that the problem is NP-complete and in proposing an efficient iterative algorithm with provable convergence properties for its solution. We discuss in detail the special case of network coordination games and its relation with the notion of cohesiveness. Finally, we show with simulations the strength of our approach with respect to naive heuristics based on classical network centrality measures

Analysis and control of agreement and disagreement opinion cascades

We introduce and analyze a continuous time and state-space model of opinion cascades on networks of large numbers of agents that form opinions about two or more options. By leveraging our recent results on the emergence of agreement and disagreement states, we introduce novel tools to analyze and control agreement and disagreement opinion cascades. New notions of agreement and disagreement centrality, which depend only on network structure, are shown to be key to characterizing the nonlinear behavior of agreement and disagreement opinion formation and cascades. Our results are relevant for the analysis and control of opinion cascades in real-world networks, including biological, social and artificial networks, and for the design of opinion-forming behaviors in robotic swarms. We illustrate an application of our model to a multi-robot task-allocation problem and discuss extensions and future directions opened by our modeling framework