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Register a new userA Two Phase Investment Game for Competitive Opinion Dynamics in Social Networks
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Added by
Swapnil Dhamal
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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We propose a setting for two-phase opinion dynamics in social networks, where a nodes final opinion in the first phase acts as its initial biased opinion in the second phase. In this setting, we study the problem of two camps aiming to maximize adoption of their respective opinions, by strategically investing on nodes in the two phases. A nodes initial opinion in the second phase naturally plays a key role in determining the final opinion of that node, and hence also of other nodes in the network due to its influence on them. More importantly, this bias also determines the effectiveness of a camps investment on that node in the second phase. To formalize this two-phase investment setting, we propose an extension of Friedkin-Johnsen model, and hence formulate the utility functions of the camps. There is a tradeoff while splitting the budget between the two phases. A lower investment in the first phase results in worse initial biases for the second phase, while a higher investment spares a lower available budget for the second phase. We first analyze the non-competitive case where only one camp invests, for which we present a polynomial time algorithm for determining an optimal way to split the camps budget between the two phases. We then analyze the case of competing camps, where we show the existence of Nash equilibrium and that it can be computed in polynomial time under reasonable assumptions. We conclude our study with simulations on real-world network datasets, in order to quantify the effects of the initial biases and the weightage attributed by nodes to their initial biases, as well as that of a camp deviating from its equilibrium strategy. Our main conclusion is that, if nodes attribute high weightage to their initial biases, it is advantageous to have a high investment in the first phase, so as to effectively influence the biases to be harnessed in the second phase.
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Analysis of opinion dynamics in social networks plays an important role in todays life. For applications such as predicting users political preference, it is particularly important to be able to analyze the dynamics of competing opinions. While observing the evolution of polar opinions of a social networks users over time, can we tell when the network behaved abnormally? Furthermore, can we predict how the opinions of the users will change in the future? Do opinions evolve according to existing network opinion dynamics models? To answer such questions, it is not sufficient to study individual user behavior, since opinions can spread far beyond users egonets. We need a method to analyze opinion dynamics of all network users simultaneously and capture the effect of individuals behavior on the global evolution pattern of the social network. In this work, we introduce Social Network Distance (SND) - a distance measure that quantifies the cost of evolution of one snapshot of a social network into another snapshot under various models of polar opinion propagation. SND has a rich semantics of a transportation problem, yet, is computable in time linear in the number of users, which makes SND applicable to the analysis of large-scale online social networks. In our experiments with synthetic and real-world Twitter data, we demonstrate the utility of our distance measure for anomalous event detection. It achieves a true positive rate of 0.83, twice as high as that of alternatives. When employed for opinion prediction in Twitter, our methods accuracy is 75.63%, which is 7.5% higher than that of the next best method. Source Code: https://cs.ucsb.edu/~victor/pub/ucsb/dbl/snd/
We study a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions. When the society contains stubborn agents with different opinions, the belief dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society fail to converge almost surely, the belief profile keeps on fluctuating in an ergodic fashion, and it converges in law to a non-degenerate random vector. The structure of the network and the location of the stubborn agents within it shape the opinion dynamics. The expected belief vector evolves according to an ordinary differential equation coinciding with the Kolmogorov backward equation of a continuous-time Markov chain with absorbing states corresponding to the stubborn agents and converges to a harmonic vector, with every regular agents value being the weighted average of its neighbors values, and boundary conditions corresponding to the stubborn agents. Expected cross-products of the agents beliefs allow for a similar characterization in terms of coupled Markov chains on the network. We prove that, in large-scale societies which are highly fluid, meaning that the product of the mixing time of the Markov chain on the graph describing the social network and the relative size of the linkages to stubborn agents vanishes as the population size grows large, a condition of emph{homogeneous influence} emerges, whereby the stationary beliefs marginal distributions of most of the regular agents have approximately equal first and second moments.
We investigate the impact of noise and topology on opinion diversity in social networks. We do so by extending well-established models of opinion dynamics to a stochastic setting where agents are subject both to assimilative forces by their local social interactions, as well as to idiosyncratic factors preventing their population from reaching consensus. We model the latter to account for both scenarios where noise is entirely exogenous to peer influence and cases where it is instead endogenous, arising from the agents desire to maintain some uniqueness in their opinions. We derive a general analytical expression for opinion diversity, which holds for any network and depends on the networks topology through its spectral properties alone. Using this expression, we find that opinion diversity decreases as communities and clusters are broken down. We test our predictions against data describing empirical influence networks between major news outlets and find that incorporating our measure in linear models for the sentiment expressed by such sources on a variety of topics yields a notable improvement in terms of explanatory power.
In this paper, we propose a generalized opinion dynamics model (GODM), which can dynamically compute each persons expressed opinion, to solve the internal opinion maximization problem for social trust networks. In the model, we propose a new, reasonable and interpretable confidence index, which is determined by both persons social status and the evaluation around him. By using the theory of diagonally dominant, we obtain the optimal analytic solution of the Nash equilibrium with maximum overall opinion. We design a novel algorithm to maximize the overall with given budget by modifying the internal opinions of people in the social trust network, and prove its optimality both from the algorithm itself and the traditional optimization algorithm-ADMM algorithms with $l_1$-regulations. A series of experiments are conducted, and the experimental results show that our method is superior to the state-of-the-art in four datasets. The average benefit has promoted $67.5%$, $83.2%$, $31.5%$, and $33.7%$ on four datasets, respectively.
Structural balance theory has been developed in sociology and psychology to explain how interacting agents, e.g., countries, political parties, opinionated individuals, with mixed trust and mistrust relationships evolve into polarized camps. Recent results have shown that structural balance is necessary for polarization in networks with fixed, strongly connected neighbor relationships when the opinion dynamics are described by DeGroot-type averaging rules. We develop this line of research in this paper in two steps. First, we consider fixed, not necessarily strongly connected, neighbor relationships. It is shown that if the network includes a strongly connected subnetwork containing mistrust, which influences the rest of the network, then no opinion clustering is possible when that subnetwork is not structurally balanced; all the opinions become neutralized in the end. In contrast, it is shown that when that subnetwork is indeed structurally balanced, the agents of the subnetwork evolve into two polarized camps and the opinions of all other agents in the network spread between these two polarized opinions. Second, we consider time-varying neighbor relationships. We show that the opinion separation criteria carry over if the conditions for fixed graphs are extended to joint graphs. The results are developed for both discrete-time and continuous-time models.
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