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Modeling Information Diffusion in Implicit Networks
"... Abstract—Social media forms a central domain for the production and dissemination of real-time information. Even though such flows of information have traditionally been thought of as diffusion processes over social networks, the underlying phenomena are the result of a complex web of interactions a ..."
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Abstract—Social media forms a central domain for the production and dissemination of real-time information. Even though such flows of information have traditionally been thought of as diffusion processes over social networks, the underlying phenomena are the result of a complex web of interactions among numerous participants. Here we develop a Linear Influence Model where rather than requiring the knowledge of the social network and then modeling the diffusion by predicting which node will influence which other nodes in the network, we focus on modeling the global influence of a node on the rate of diffusion through the (implicit) network. We model the number of newly infected nodes as a function of which other nodes got infected in the past. For each node we estimate an influence function that quantifies how many subsequent infections can be attributed to the influence of that node over time. A nonparametric formulation of the model leads to a simple least squares problem that can be solved on large datasets. We validate our model on a set of 500 million tweets and a set of 170 million news articles and blog posts. We show that the Linear Influence Model accurately models influences of nodes and reliably predicts the temporal dynamics of information diffusion. We find that patterns of influence of individual participants differ significantly depending on the type of the node and the topic of the information. I.
Networks in Finance
- In The Network
, 2009
"... Abstract Modern …nancial systems exhibit a high degree of interdependence. There are different possible sources of connections between …nancial institutions, stemming from both the asset and the liability side of their balance sheet. For instance, banks are directly connected through mutual exposur ..."
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Abstract Modern …nancial systems exhibit a high degree of interdependence. There are different possible sources of connections between …nancial institutions, stemming from both the asset and the liability side of their balance sheet. For instance, banks are directly connected through mutual exposures acquired on the interbank market. Likewise, holding similar portfolios or sharing the same mass of depositors creates indirect linkages between …nancial institutions. Broadly understood as a collection of nodes and links between nodes, networks can be a useful representation of …nancial systems. By providing means to model the speci…cs of economic interactions, network analysis can better explain certain economic phenomena. In this paper we argue that the use of network theories can enrich our understanding of …nancial systems. We review the recent developments in …nancial networks, highlighting the synergies created from applying network theory to answer …nancial questions. Further, we propose several directions of research. First, we consider the issue of systemic risk. In this context, two questions arise: how resilient …nancial networks are to contagion, and how …nan-cial institutions form connections when exposed to the risk of contagion. The second issue we consider is how network theory can be used to explain freezes in the interbank market of the type we have observed in August 2007 and subsequently. The third issue is how social networks can improve investment decisions and corporate governance. Recent empirical work has provided some interesting results in this regard. The fourth issue concerns the role of networks in distributing primary issues of securities as, for example, in initial public o¤erings, or seasoned debt and equity issues. Finally, we consider the role of networks as a form of mutual monitoring as in micro…nance.
How bad is forming your own opinion
- In Proc. 52nd IEEE Symposium on Foundations of Computer Science
, 2011
"... A long-standing line of work in economic theory has studied models by which a group of people in a social network, each holding a numerical opinion, can arrive at a shared opinion through repeated averaging with their neighbors in the network. Motivated by the observation that consensus is rarely re ..."
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A long-standing line of work in economic theory has studied models by which a group of people in a social network, each holding a numerical opinion, can arrive at a shared opinion through repeated averaging with their neighbors in the network. Motivated by the observation that consensus is rarely reached in real opinion dynamics, we study a related sociological model in which individuals ’ intrinsic beliefs counterbalance the averaging process and yield a diversity of opinions. By interpreting the repeated averaging as best-response dynamics in an underlying game with natural payoffs, and the limit of the process as an equilibrium, we are able to study the cost of disagreement in these models relative to a social optimum. We provide a tight bound on the cost at equilibrium relative to the optimum; our analysis draws a connection between these agreement models and extremal problems for generalized eigenvalues. We also consider a natural network design problem in this setting, where adding links to the underlying network can reduce the cost of disagreement at equilibrium.
Control of preferences in social networks
- in Decision and Control (CDC), 2010 49th IEEE Conference on
, 2010
"... Abstract — We consider the problem of deriving optimal advertising policies for the spread of innovations in a social network. We seek to compute policies that account for i) endogenous network influences, ii) the presence of competitive firms, that also wish to influence the network, and iii) possi ..."
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Abstract — We consider the problem of deriving optimal advertising policies for the spread of innovations in a social network. We seek to compute policies that account for i) endogenous network influences, ii) the presence of competitive firms, that also wish to influence the network, and iii) possible uncertainties in the network model. Contrary to prior work in optimal advertising, which also accounts for network influences, we assume a dynamic model of preferences and we compute optimal policies for either finite or infinite horizons. We also compute robust optimal policies in the case where the evolution of preferences is also affected by external disturbances. Finally, in the presence of a competitive firm, we compute optimal Stackelberg and Nash solutions. I.
Community Structure and Market Outcomes: A Repeated Games in Networks Approach
, 2010
"... Consider a large market with asymmetric information, in which sellers choose whether to cooperate or deviate and ‘cheat’ their buyers, and buyers decide whether to re-purchase from different sellers. We model active trade relationships as links in a buyer-seller network and suggest a framework for s ..."
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Cited by 8 (2 self)
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Consider a large market with asymmetric information, in which sellers choose whether to cooperate or deviate and ‘cheat’ their buyers, and buyers decide whether to re-purchase from different sellers. We model active trade relationships as links in a buyer-seller network and suggest a framework for studying repeated games in such networks. In our framework, buyers and sellers have rich yet incomplete knowledge of the network structure; allowing us to derive meaningful conditions that determine whether a network is consistent with trade and cooperation between every buyer and seller that are connected. We show that three network features reduce the minimal discount factor necessary for sustaining cooperation: moderate competition, sparseness, and segregation. We find that the incentive constraints rule out networks that maximize the volume of trade and that the constrained trade maximizing networks are in between ‘old world’ segregated and sparse networks, and a ‘global market’.
Convergence of Rule-of-Thumb Learning Rules in Social Networks
"... Abstract — We study the problem of dynamic learning by a social network of agents. Each agent receives a signal about an underlying state and communicates with a subset of agents (his neighbors) in each period. The network is connected. In contrast to the majority of existing learning models, we foc ..."
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Abstract — We study the problem of dynamic learning by a social network of agents. Each agent receives a signal about an underlying state and communicates with a subset of agents (his neighbors) in each period. The network is connected. In contrast to the majority of existing learning models, we focus on the case where the underlying state is time-varying. We consider the following class of rule of thumb learning rules: at each period, each agent constructs his posterior as a weighted average of his prior, his signal and the information he receives from neighbors. The weights given to signals can vary over time and the weights given to neighbors can vary across agents. We distinguish between two subclasses: (1) constant weight rules; (2) diminishing weight rules. The latter reduces weights given to signals asymptotically to 0. Our main results characterize the asymptotic behavior of beliefs. We show that the general class of rules leads to unbiased estimates of the underlying state. When the underlying state has innovations with variance tending to zero asymptotically, we show that the diminishing weight rules ensure convergence in the mean-square sense. In contrast, when the underlying state has persistent innovations, constant weight rules enable us to characterize explicit bounds on the mean square error between an agent’s belief and the underlying state as a function of the type of learning rule and signal structure. I.
On approximations and ergodicity classes in random chains
- IEEE Trans. on Automatic
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How Homophily Affects Diffusion and Learning in Networks
, 2010
"... We examine how diffusion and learning processes are influenced by network properties, focusing on density and homophily – the tendency of agents to associate disproportionately with those sharing similar traits. Homophily does not affect the speed of diffusions that travel along shortest paths; thei ..."
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Cited by 6 (1 self)
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We examine how diffusion and learning processes are influenced by network properties, focusing on density and homophily – the tendency of agents to associate disproportionately with those sharing similar traits. Homophily does not affect the speed of diffusions that travel along shortest paths; their rate is determined only by the size of the society and the number of links per agent. In contrast, homophily substantially slows learning based on repeated averaging of neighbors’ information. Our analysis shows that changing a network can have widely different effects on information flow depending on the details of the transmission process and we provide general tools for analyzing such changes.
Heterogeneous beliefs and local information in stochastic fictitious play
- Games and Economic Behavior
, 2008
"... Stochastic …ctitious play (SFP) assumes that agents do not try to in‡uence the future play of their current opponents, an assumption that is justi…ed by appeal to a setting with a large population of players who are randomly matched to play the game. However, the dynamics of SFP have only been analy ..."
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Cited by 5 (1 self)
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Stochastic …ctitious play (SFP) assumes that agents do not try to in‡uence the future play of their current opponents, an assumption that is justi…ed by appeal to a setting with a large population of players who are randomly matched to play the game. However, the dynamics of SFP have only been analyzed in models where all agents in a player role have the same beliefs. We analyze the dynamics of SFP in settings where there is a population of agents who observe only outcomes in their own matches and thus have heterogeneous beliefs. We provide conditions that ensure that the system converges to a state with homogeneous beliefs, and that its asymptotic behavior is the same as with a single representative agent in each player role. We thank Michel Benaïm. Josef Hofbauer, and William Sandholm for very helpful comments and suggestions. 1 1
Threshold learning dynamics in social networks
- PLoS ONE
, 2011
"... Social learning is defined as the ability of a population to aggregate information, a process which must crucially depend on the mechanisms of social interaction. Consumers choosing which product to buy, or voters deciding which option to take with respect to an important issue, typically confront e ..."
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Social learning is defined as the ability of a population to aggregate information, a process which must crucially depend on the mechanisms of social interaction. Consumers choosing which product to buy, or voters deciding which option to take with respect to an important issue, typically confront external signals to the information gathered from their contacts. Economic models typically predict that correct social learning occurs in large populations unless some individuals display unbounded influence. We challenge this conclusion by showing that an intuitive threshold process of individual adjustment does not always lead to such social learning. We find, specifically, that three generic regimes exist separated by sharp discontinuous transitions. And only in one of them, where the threshold is within a suitable intermediate range, the population learns the correct information. In the other two, where the threshold is either too high or too low, the system either freezes or enters into persistent flux, respectively. These regimes are generally observed in different social networks (both complex or regular), but limited interaction is found to promote correct learning by enlarging the parameter region where it occurs.
