Theoretical models suggest that social networks influence the evolution of cooperation, but to date there have been few experimental studies. Observational data suggest that a wide variety of behaviors may spread in human social networks, but subjects in such studies can choose to befriend people with similar behaviors, posing difficulty for causal inference. Here, we exploit a seminal set of laboratory experiments that originally showed that voluntary costly punishment can help sustain cooperation. In these experiments, subjects were randomly assigned to a sequence of different groups in order to play a series of single-shot public goods games with strangers; this feature allowed us to draw networks of interactions to explore how cooperative and uncooperative behavior spreads from person to person to person. We show that, in both an ordinary public goods game and in a public goods game with punishment, focal individuals are influenced by fellow group members' contribution behavior in future interactions with other individuals who were not a party to the initial interaction. Furthermore, this influence persists for multiple periods and spreads up to three degrees of separation (from person to person to person to person). The results suggest that each additional contribution a subject makes to the public good in the first period is tripled over the course of the experiment by other subjects who are directly or indirectly influenced to contribute more as a consequence. These are the first results to show experimentally that cooperative behavior cascades in human social networks.
Cascades represent an important phenomenon across various disciplines such as sociology, economy, psychology, political science, marketing, and epidemiology. An important property of cascades is their morphology, which encompasses the structure, shape, and size. However, cascade morphology has not been rigorously characterized and modeled in prior literature. In this paper, we propose a Multi-order Markov Model for the Morphology of Cascades ($M^4C$) that can represent and quantitatively characterize the morphology of cascades with arbitrary structures, shapes, and sizes. $M^4C$ can be used in…
Recent studies suggest that cooperative decision-making in one-shot interactions is a history-dependent dynamic process: promoting intuition versus deliberation has typically a positive effect on cooperation (dynamism) among people living in a cooperative setting and with no previous experience in economic games on cooperation (history-dependence). Here we report on a lab experiment exploring how these findings transfer to a non-cooperative setting. We find two major results: (i) promoting intuition versus deliberation has no effect on cooperative behavior among inexperienced subjects living i…
Misinformation and rumor can spread rapidly and widely through online social networks and therefore rumor controlling has become a critical issue. It is often assumed that there is a single authority whose goal is to minimize the spread of rumor by generating a positive cascade. In this paper, we study a more realistic scenario when there are multiple positive cascades generated by different agents. For the multiple-cascade diffusion, we propose the P2P independent cascade (PIC) model for private social communications. The main part of this paper is an analysis of the rumor blocking effect (i.…
A recently introduced concept of "cooperative equilibrium", based on the assumption that players have a natural attitude to cooperation, has been proven a powerful tool in predicting human behaviour in social dilemmas. In this paper, we extend this idea to more general game models, termed "Pareto solvable" games, which in particular include the Nash Bargaining Problem and the Ultimatum Game. We show that games in this class possess a unique pure cooperative equilibrium. Furthermore, for the Ultimatum Game, this notion appears to be strongly correlated with a suitably defined variant of the Dic…
Cooperation is widespread in human societies, but its maintenance at the group level remains puzzling if individuals benefit from not cooperating. Explanations of the maintenance of cooperation generally assume that cooperative and non-cooperative behavior in others can be assessed and copied accurately. However, humans have a well known capacity to deceive and thus to manipulate how others assess their behavior. Here, we show that hypocrisy - claiming to be acting cooperatively while acting selfishly - can maintain social cooperation because it prevents the spread of selfish behavior. We demo…
A new approach for the description of phenomena of social aggregation is suggested. On the basis of psychological concepts (as for instance social norms and cultural coordinates), we deduce a general mechanism for the social aggregation in which different clusters of individuals can merge according to the cooperation among the agents. In their turn, the agents can cooperate or defect according to the clusters distribution inside the system. The fitness of an individual increases with the size of its cluster, but decreases with the work the individual had to do in order to join it. In order to …
Georgia Institute of Technology（佐治亚理工学院）；Insight Data Science（Insight数据科学公司）
The global dynamics of event cascades are often governed by the local dynamics of peer influence. However, detecting social influence from observational data is challenging due to confounds like homophily and practical issues like missing data. We propose a simple discriminative method to detect influence from observational data. The core of the approach is to train a ranking algorithm to predict the source of the next event in a cascade, and compare its out-of-sample accuracy against a competitive baseline which lacks access to features corresponding to social influence. We analyze synthetica…
Cooperative behaviors are common in humans and are fundamental to our society. Theoretical and experimental studies have modeled environments in which the behaviors of humans, or agents, have been restricted to analyze their social behavior. However, it is important that such studies are generalized to less restrictive environments to understand human society. Social network games (SNGs) provide a particularly powerful tool for the quantitative study of human behavior. In SNGs, numerous players can behave more freely than in the environments used in previous studies; moreover, their relationsh…
When a piece of information (microblog, photograph, video, link, etc.) starts to spread in a social network, an important question arises: will it spread to viral proportions - where viral can be defined as an order-of-magnitude increase. However, several previous studies have established that cascade size and frequency are related through a power-law - which leads to a severe imbalance in this classification problem. In this paper, we devise a suite of measurements based on structural diversity - the variety of social contexts (communities) in which individuals partaking in a given cascade en…
A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple {\it initiators} trigger the cascade, and where all nodes possess the same adoption threshold $ϕ$. Specifically, using empirical and stylized models of social networks, we study cascade size as a function of the initiator fraction $p$. We find that even for arbitrarily high value of $ϕ$, there exists a critical initiator fraction $p_c(ϕ)$ beyond which the cascade becomes global. Network structure, in particul…
Large cascades can develop in online social networks as people share information with one another. Though simple reshare cascades have been studied extensively, the full range of cascading behaviors on social media is much more diverse. Here we study how diffusion protocols, or the social exchanges that enable information transmission, affect cascade growth, analogous to the way communication protocols define how information is transmitted from one point to another. Studying 98 of the largest information cascades on Facebook, we find a wide range of diffusion protocols - from cascading reshare…
Threshold models of cascades in the social sciences and economics explain the spread of opinion and innovation due to social influence. In threshold cascade models, fads or innovations spread between agents as determined by their interactions with other agents and their personal threshold of resistance. Typically, these models do not account for structure in the timing of interaction between the units. In this work, we extend a model of social cascades by Duncan Watts to temporal interaction networks. In our model, we assume friends and acquaintances influence agents for a certain time into th…
Cooperative behavior in real social dilemmas is often perceived as a phenomenon emerging from norms and punishment. To overcome this paradigm, we highlight the interplay between the influence of social networks on individuals, and the activation of spontaneous self-regulating mechanisms, which may lead them to behave cooperatively, while interacting with others and taking conflicting decisions over time. By extending Evolutionary game theory over networks, we prove that cooperation partially or fully emerges whether self-regulating mechanisms are sufficiently stronger than social pressure. Int…
In a diversified context with multiple social networking sites, heterogeneous activity patterns and different user-user relations, the concept of "information cascade" is all but univocal. Despite the fact that such information cascades can be defined in different ways, it is important to check whether some of the observed patterns are common to diverse contagion processes that take place on modern social media. Here, we explore one type of information cascades, namely, those that are time-constrained, related to two kinds of socially-rooted topics on Twitter. Specifically, we show that in bot…
In the last few decades, numerous experiments have shown that humans do not always behave so as to maximize their material payoff. Cooperative behavior when non-cooperation is a dominant strategy (with respect to the material payoffs) is particularly puzzling. Here we propose a novel approach to explain cooperation, assuming what Halpern and Pass (2013) call "translucent players". Typically, players are assumed to be "opaque", in the sense that a deviation by one player does not affect the strategies used by other players. But a player may believe that if he switches from one strategy to anoth…
Recent grassroots movements have suggested that online social networks might play a key role in their organization, as adherents have a fast, many-to-many, communication channel to help coordinate their mobilization. The structure and dynamics of the networks constructed from the digital traces of protesters have been analyzed to some extent recently. However, less effort has been devoted to the analysis of the semantic content of messages exchanged during the protest. Using the data obtained from a microblogging service during the brewing and active phases of the 15M movement in Spain, we per…
With the passage of time, the development of communication technology and transportation broke the isolation among people. Relationship tends to be complicated, pluralism, dynamism. In the network where interpersonal relationship and evolved complex net based on game theory work serve respectively as foundation architecture and theoretical model, with the combination of game theory and regard public welfare as influencing factor, we artificially initialize that closed network system. Through continual loop operation of the program, we summarize the changing rule of the cooperative behavior in …
Traces of user activities recorded in online social networks such as the creation, viewing and forwarding/sharing of information over time open new possibilities to quantitatively and systematically understand the information diffusion process on social networks. From an online social network like WeChat, we could collect a large number of information cascade trees, each of which tells the spreading trajectory of a message/information such as which user creates the information and which users view or forward the information shared by which neighbors. In this work, we propose two heterogeneous …
Fads, product adoption, mobs, rumors, memes, and emergent norms are diverse social contagions that have been modeled as network cascades. Empirical study of these cascades is vulnerable to what we describe as the "opacity problem": the inability to observe the critical level of peer influence required to trigger an individual's behavioral change. Even with maximal information, network cascades reveal intervals that bound critical levels of peer exposure, rather than critical values themselves. Existing practice uses interval maxima, which systematically over-estimates the social influence requ…
How does information flow in online social networks? How does the structure and size of the information cascade evolve in time? How can we efficiently mine the information contained in cascade dynamics? We approach these questions empirically and present an efficient and scalable mathematical framework for quantitative analysis of cascades on networks. We define a cascade generating function that captures the details of the microscopic dynamics of the cascades. We show that this function can also be used to compute the macroscopic properties of cascades, such as their size, spread, diameter, n…
Cascades of information-sharing are a primary mechanism by which content reaches its audience on social media, and an active line of research has studied how such cascades, which form as content is reshared from person to person, develop and subside. In this paper, we perform a large-scale analysis of cascades on Facebook over significantly longer time scales, and find that a more complex picture emerges, in which many large cascades recur, exhibiting multiple bursts of popularity with periods of quiescence in between. We characterize recurrence by measuring the time elapsed between bursts, th…
Information propagation in online social networks is facilitated by two types of influence - endogenous (peer) influence that acts between users of the social network and exogenous (external) that corresponds to various external mediators such as online news media. However, inference of these influences from data remains a challenge, especially when data on the activation of users is scarce. In this paper we propose a methodology that yields estimates of both endogenous and exogenous influence using only a social network structure and a single activation cascade. Our method exploits the statis…
We investigate two paradigms for studying the evolution of cooperation--Prisoner's Dilemma and Snowdrift game in an online friendship network obtained from a social networking site. We demonstrate that such social network has small-world property and degree distribution has a power-law tail. Besides, it has hierarchical organizations and exhibits disassortative mixing pattern. We study the evolutionary version of the two types of games on it. It is found that enhancement and sustainment of cooperative behaviors are attributable to the underlying network topological organization. It is also sho…
Modelling information cascades over online social networks is important in fields from marketing to civil unrest prediction, however the underlying network structure strongly affects the probability and nature of such cascades. Even with simple cascade dynamics the probability of large cascades are almost entirely dictated by network properties, with well-known networks such as Erdos-Renyi and Barabasi-Albert producing wildly different cascades from the same model. Indeed, the notion of 'superspreaders' has arisen to describe highly influential nodes promoting global cascades in a social netwo…
Information spreading is an interesting field in the domain of online social media. In this work, we are investigating how well different seed selection strategies affect the spreading processes simulated using independent cascade model on eighteen multilayer social networks. Fifteen networks are built based on the user interaction data extracted from Facebook public pages and tree of them are multilayer networks downloaded from public repository (two of them being Twitter networks). The results indicate that various state of the art seed selection strategies for single-layer networks like K-S…
In Evolutionary Dynamics the understanding of cooperative phenomena in natural and social systems has been the subject of intense research during decades. We focus attention here on the so-called "Lattice Reciprocity" mechanisms that enhance evolutionary survival of the cooperative phenotype in the Prisoner's Dilemma game when the population of darwinian replicators interact through a fixed network of social contacts. Exact results on a "Dipole Model" are presented, along with a mean-field analysis as well as results from extensive numerical Monte Carlo simulations. The theoretical framework u…
By means of extensive computer simulations, the authors consider the entangled coevolution of actions and social structure in a new version of a spatial Prisoner's Dilemma model that naturally gives way to a process of social differentiation. Diverse social roles emerge from the dynamics of the system: leaders are individuals getting a large payoff who are imitated by a considerable fraction of the population, conformists are unsatisfied cooperative agents that keep cooperating, and exploiters are defectors with a payoff larger than the average one obtained by cooperators. The dynamics generat…
The network-based model of social contagion has revolved around information on local interactions; its central focus has been on network topological properties shaping the local interactions and, ultimately, social contagion outcomes. We extend this approach by introducing information on the global state, or global information, into the network-based model and analyzing how it alters social contagion dynamics in six different classes of networks: a two-dimensional square lattice, small-world networks, Erdős-Rényi networks, regular random networks, Holme-Kim networks, and Barabási-Albert networ…
The ability to understand and eventually predict the emergence of information and activation cascades in social networks is core to complex socio-technical systems research. However, the complexity of social interactions makes this a challenging enterprise. Previous works on cascade models assume that the emergence of this collective phenomenon is related to the activity observed in the local neighborhood of individuals, but do not consider what determines the willingness to spread information in a time-varying process. Here we present a mechanistic model that accounts for the temporal evoluti…
The conflict between pro-self and pro-social behaviour is at the core of many key problems of our time, as, for example, the reduction of air pollution and the redistribution of scarce resources. For the well-being of our societies, it is thus crucial to find mechanisms to promote pro-social choices over egoistic ones. Particularly important, because cheap and easy to implement, are those mechanisms that can change people's behaviour without forbidding any options or significantly changing their economic incentives, the so-called "nudges". Previous research has found that moral nudges (e.g., m…
The construction of reciprocal relationships requires cooperative interactions during the initial meetings. However, cooperative behavior with strangers is risky because the strangers may be exploiters. In this study, we show that people increase the likelihood of cooperativeness of strangers by using lightweight non-risky interactions in risky situations based on the analysis of a social network game (SNG). They can construct reciprocal relationships in this manner. The interactions involve low-cost signaling because they are not generated at any cost to the senders and recipients. Theoretica…
Theoretical progress in understanding the dynamics of spreading processes on graphs suggests the existence of an epidemic threshold below which no epidemics form and above which epidemics spread to a significant fraction of the graph. We have observed information cascades on the social media site Digg that spread fast enough for one initial spreader to infect hundreds of people, yet end up affecting only 0.1% of the entire network. We find that two effects, previously studied in isolation, combine cooperatively to drastically limit the final size of cascades on Digg. First, because of the high…
Cascade models on networks have been used extensively to study cascade failure in complex systems. However, most current models consider failure caused by node damage and neglect the possibility of link damage, which is relevant to transportation, social dynamics, biology, and medicine. In an attempt to generalize conventional cascade models to link damage, we propose a link cascade model based on the standard independent cascade model, which is then solved via both numerical simulation and analytic approximation. We find that the probability that a node loses all its links due to link damage …
Information cascades are ubiquitous in various social networking web sites. What mechanisms drive information diffuse in the networks? How does the structure and size of the cascades evolve in time? When and which users will adopt a certain message? Approaching these questions can considerably deepen our understanding about information cascades and facilitate various vital applications, including viral marketing, rumor prevention and even link prediction. Most previous works focus only on the final cascade size prediction. Meanwhile, they are always cascade graph dependent methods, which make …
With the emergence and rapid proliferation of social media platforms and social networking sites, recent years have witnessed a surge of misinformation spreading in our daily life. Drawing on a large-scale dataset which covers more than 1.4M posts and 18M comments, we investigate the propagation of two distinct narratives--(i) conspiracy information, whose claims are generally unsubstantiated and thus referred as misinformation to some extent, and (ii) scientific information, whose origins are generally readily identifiable and verifiable--in an online social media platform. We find that consp…
Models of cooperation grounded on social networks and on the ability of individuals to choose actions and partners aim to describe human social behavior. Extensive computer simulations of these models give important insight in the social mechanisms behind emerging collective behavior. We consider the entangled co-evolution of actions and social structure in a new version of a spatial Prisoner's Dilemma model that naturally gives way to a process of social differentiation. Diverse social roles emerge from the dynamics of the system: leaders -individuals getting a large payoff who are imitated b…
The emergence of cooperation in the thermodynamic limit of social dilemmas is an emerging field of research. While numerical approaches (using replicator dynamics) are dime a dozen, analytical approaches are rare. A particularly useful analytical approach is to utilize a mapping between the spin-1/2 Ising model in 1-D and the social dilemma game and calculate the magnetization, which is the net difference between the fraction of cooperators and defectors in a social dilemma. In this paper, we look at the susceptibility, which probes the net change in the fraction of players adopting a certain …
In this paper we study how the network of agents adopting a particular technology relates to the structure of the underlying network over which the technology adoption spreads. We develop a model and show that the network of agents adopting a particular technology may have characteristics that differ significantly from the social network of agents over which the technology spreads. For example, the network induced by a cascade may have a heavy-tailed degree distribution even if the original network does not. This provides evidence that online social networks created by technology adoption over…
Citation cascades in blog networks are often considered as traces of information spreading on this social medium. In this work, we question this point of view using both a structural and semantic analysis of five months activity of the most representative blogs of the french-speaking community.Statistical measures reveal that our dataset shares many features with those that can be found in the literature, suggesting the existence of an identical underlying process. However, a closer analysis of the post content indicates that the popular epidemic-like descriptions of cascades are misleading in…
The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We accomplish this by employing a truncated normal distribution of the nodes' thresholds and observe a non-monotonic change in the cascade size as we vary the standard deviation.…
Threshold cascade models have been used to describe spread of behavior in social networks and cascades of default in financial networks. In some cases, these networks may have multiple kinds of interactions, such as distinct types of social ties or distinct types of financial liabilities; furthermore, nodes may respond in different ways to in influence from their neighbors of multiple types. To start to capture such settings in a stylized way, we generalize a threshold cascade model to a multiplex network in which nodes follow one of two response rules: some nodes activate when, in at least on…
Widespread interest in the diffusion of information through social networks has produced a large number of Social Dynamics models. A majority of them use theoretical hypothesis to explain their diffusion mechanisms while the few empirically based ones average out their measures over many messages of different content. Our empirical research tracking the step-by-step email propagation of an invariable viral marketing message delves into the content impact and has discovered new and striking features. The topology and dynamics of the propagation cascades display patterns not inherited from the e…
Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex networks. We generalize the threshold cascade model [D. J. Watts, Proc. Natl. Acad. Sci. U.S.A. 99, 5766 (2002)] to multiplex networks, in which a node activates if a sufficiently large fraction of neighbors in any layer are active. We show that both combining layers (i.e., realizing other interactions play a role) and splitting a network into layers (i.e., recogni…
A characteristic property of networks is their ability to propagate influences, such as infectious diseases, behavioral changes, and failures. An especially important class of such contagious dynamics is that of cascading processes. These processes include, for example, cascading failures in infrastructure systems, extinctions cascades in ecological networks, and information cascades in social systems. In this review, we discuss recent progress and challenges associated with the modeling, prediction, detection, and control of cascades in networks.
Online social networks (OSN) are prime examples of socio-technical systems in which individuals interact via a technical platform. OSN are very volatile because users enter and exit and frequently change their interactions. This makes the robustness of such systems difficult to measure and to control. To quantify robustness, we propose a coreness value obtained from the directed interaction network. We study the emergence of large drop-out cascades of users leaving the OSN by means of an agent-based model. For agents, we define a utility function that depends on their relative reputation and t…
Adoption of innovations, products or online services is commonly interpreted as a spreading process driven to large extent by social influence and conditioned by the needs and capacities of individuals. To model this process one usually introduces behavioural threshold mechanisms, which can give rise to the evolution of global cascades if the system satisfies a set of conditions. However, these models do not address temporal aspects of the emerging cascades, which in real systems may evolve through various pathways ranging from slow to rapid patterns. Here we fill this gap through the analysis…
When a piece of information (microblog, photograph, video, link, etc.) starts to spread in a social network, an important question arises: will it spread to "viral" proportions -- where "viral" is defined as an order-of-magnitude increase. However, several previous studies have established that cascade size and frequency are related through a power-law - which leads to a severe imbalance in this classification problem. In this paper, we devise a suite of measurements based on "structural diversity" -- the variety of social contexts (communities) in which individuals partaking in a given cascad…
Most social network sites allow users to reshare a piece of information posted by a user. As time progresses, the cascade of reshares grows, eventually saturating after a certain time period. While previous studies have focused heavily on one aspect of the cascade phenomenon, specifically predicting when the cascade would go viral, in this paper, we take a more holistic approach by analyzing the occurrence of two events within the cascade lifecycle - the period of maximum growth in terms of surge in reshares and the period where the cascade starts declining in adoption. We address the challeng…
University of Pisa（比萨大学）；ICAR-CNR（意大利国家研究委员会信息与高性能计算研究所）；Sapienza University（罗马大学）；ISI Foundation（ISI基金会）；CENTAI（CENTAI研究所）；Eurecat（加泰罗尼亚技术中心）
Despite echo chambers in social media have been under considerable scrutiny, general models for their detection and analysis are missing. In this work, we aim to fill this gap by proposing a probabilistic generative model that explains social media footprints -- i.e., social network structure and propagations of information -- through a set of latent communities, characterized by a degree of echo-chamber behavior and by an opinion polarity. Specifically, echo chambers are modeled as communities that are permeable to pieces of information with similar ideological polarity, and impermeable to in…
Self-reinforcing cascades: A spreading model for beliefs or products of varying intensity or quality
University of Vermont（佛蒙特大学）；Vermont Complex Systems Institute, University of Vermont（佛蒙特大学佛蒙特复杂系统研究所）；Santa Fe Institute（圣塔菲研究所）；Department of Computer Science, University of Vermont（佛蒙特大学计算机科学系）；MACSI, Department of Mathematics and Statistics, University of Limerick（利默里克大学数学与统计系MACSI）；Department of Physics, Boston University（波士顿大学物理系）
Understanding the neural mechanisms responsible for human social interactions is difficult, since the brain activities of two or more individuals have to be examined simultaneously and correlated with the observed social patterns. We introduce the concept of hyper-brain network, a connectivity pattern representing at once the information flow among the cortical regions of a single brain as well as the relations among the areas of two distinct brains. Graph analysis of hyper-brain networks constructed from the EEG scanning of 26 couples of individuals playing the Iterated Prisoner's Dilemma rev…
