Effects of Time Horizons on Influence Maximization in the Voter Dynamics

In this paper we analyze influence maximization in the voter model with an active strategic and a passive influencing party in non-stationary settings. We thus explore the dependence of optimal influence allocation on the time horizons of the strategic influencer. We find that on undirected heterogeneous networks, for short time horizons, influence is maximized when targeting low-degree nodes, while for long time horizons influence maximization is achieved when controlling hub nodes. Furthermore, we show that for short and intermediate time scales influence maximization can exploit knowledge of (transient) opinion configurations. More in detail, we find two rules. First, nodes with states differing from the strategic influencer's goal should be targeted. Second, if only few nodes are initially aligned with the strategic influencer, nodes subject to opposing influence should be avoided, but when many nodes are aligned, an optimal influencer should shadow opposing influence.Comment: 22 page

Resisting Influence: How the Strength of Predispositions to Resist Control Can Change Strategies for Optimal Opinion Control in the Voter Model

In this paper we investigate influence maximization, or optimal opinion control, in a modified version of the two-state voter dynamics in which a native state and a controlled or influenced state are accounted for. We include agent predispositions to resist influence in the form of a probability $q$ with which agents spontaneously switch back to the native state when in the controlled state. We argue that in contrast to the original voter model, optimal control in this setting depends on $q$: For low strength of predispositions $q$ optimal control should focus on hub nodes, but for large $q$ optimal control can be achieved by focusing on the lowest degree nodes. We investigate this transition between hub and low-degree node control for heterogeneous undirected networks and give analytical and numerical arguments for the existence of two control regimes

Transmission errors and influence maximization in the voter model

In this paper we analyze the effects of mistakes in opinion propagation in the voter model on strategic influence maximization. We provide numerical results and analytical arguments to show that generally two regimes exist for optimal opinion control: a regime of low transmission errors in which influence maximizers should focus on hub nodes and a large-error regime in which influence maximizers should focus on low-degree nodes. We also develop a degree-based mean-field theory and apply it to random networks with bimodal degree distribution, finding that analytical results for the dependence of regimes on parameters qualitatively agree with numerical results for scale-free networks. We generally find that the regime of optimal hub control is the larger, the more heterogeneous the social network and the smaller the more resources both available to the influencers

Statistical properties of volume and calendar effects in prediction markets

Prediction markets have proven to be an exceptional tool for harnessing the "wisdom of the crowd", consequently making accurate forecasts about future events. Motivated by the lack of quantitative means of validations for models of prediction markets, in this paper we analyze the statistical properties of volume as well as the seasonal regularities (i.e., calendar effects) shown by volume and price. To accomplish this, we use a set of 3385 prediction market time series provided by PredictIt. We find that volume, with the exception of its seasonal regularities, possesses different properties than what is observed in financial markets. Moreover, price does not seem to exhibit any calendar effect. These findings suggest a significant difference between prediction and financial markets, and offer evidence for the need of studying prediction markets in more detail.<br/

Network-based indicators of Bitcoin bubbles

The functioning of the cryptocurrency Bitcoin relies on the open availability of the entire history of its transactions. This makes it a particularly interesting socio-economic system to analyse from the point of view of network science. Here we analyse the evolution of the network of Bitcoin transactions between users. We achieve this by using the complete transaction history from December 5th 2011 to December 23rd 2013. This period includes three bubbles experienced by the Bitcoin price. In particular, we focus on the global and local structural properties of the user network and their variation in relation to the different period of price surge and decline. By analysing the temporal variation of the heterogeneity of the connectivity patterns we gain insights on the different mechanisms that take place during bubbles, and find that hubs (i.e., the most connected nodes) had a fundamental role in triggering the burst of the second bubble. Finally, we examine the local topological structures of interactions between users, we discover that the relative frequency of triadic interactions experiences a strong change before, during and after a bubble, and suggest that the importance of the hubs grows during the bubble. These results provide further evidence that the behaviour of the hubs during bubbles significantly increases the systemic risk of the Bitcoin network, and discuss the implications on public policy interventions

Efficient Influence Maximization Under Network Uncertainty

We consider the influence maximization (IM) problem in a partially visible social network. The goal is to design a decision-making framework for an autonomous agent to select a limited set of influential seed nodes to spread a message as widely as possible across the network. We consider the realistic case where only a partial section of the network is visible to the agent, while the rest is one of a finite set of known structures, each with a given realization probability. We show that solving the IM problem in this setting is NP-hard, and we provide analytical guarantees for the performance of a novel computationally-efficient seed-selection approximation algorithm for the agent. In empirical experiments on real-world social networks, we demonstrate the efficiency of our scheme and show that it outperforms state-of-the-art approaches that do not model the uncertainty