Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.

/pdf/maximizing-the-spread-of-influence-through-a-social-network-3nnj0jic76.pdf

Maximizing the spread of influence through a social network

Though word-of-mouth (w-o-m) communications is a pervasive and intriguing phenomenon, little is known on its underlying process of personal communications. Moreover as marketers are getting more interested in harnessing the power of w-o-m, for e-business and other net related activities, the effects of the different communications types on macro level marketing is becoming critical. In particular we are interested in the breakdown of the personal communication between closer and stronger communications that are within an individual's own personal group (strong ties) and weaker and less personal communications that an individual makes with a wide set of other acquaintances and colleagues (weak ties). We use a technique borrowed from Complex Systems Analysis called stochastic cellular automata in order to generate data and analyze the results so that answers to our main research issues could be ascertained. The following summarizes the impact of strong and weak ties on the speed of acceptance of a new product: ••The influence of weak ties is at least as strong as the influence of strong ties. Despite the relative inferiority of the weak tie parameter in the model's assumptions, their effect approximates or exceeds that of strong ties, in all stages of the product life cycle. ••External marketing efforts (e.g., advertising) are effective. However, beyond a relatively early stage of the growth cycle of the new product, their efficacy quickly diminishes and strong and weak ties become the main forces propelling growth. The results clearly indicate that information dissemination is dominated by both weak and strong w-o-m, rather than by advertising. ••The effect of strong ties diminishes as personal network size decreases. Market attributes were also found to mediate the effects of weak and strong ties. When personal networks are small, weak ties were found to have a stronger impact on information dissemination than strong ties.

https://www.jstor.org/stable/pdfplus/40216600.pdf

Talk of the Network: A Complex Systems Look at the Underlying Process of Word-of-Mouth

Recently, there has been tremendous interest in the phenomenon of influence propagation in social networks. The studies in this area assume they have as input to their problems a social graph with edges labeled with probabilities of influence between users. However, the question of where these probabilities come from or how they can be computed from real social network data has been largely ignored until now. Thus it is interesting to ask whether from a social graph and a log of actions by its users, one can build models of influence. This is the main problem attacked in this paper. In addition to proposing models and algorithms for learning the model parameters and for testing the learned models to make predictions, we also develop techniques for predicting the time by which a user may be expected to perform an action. We validate our ideas and techniques using the Flickr data set consisting of a social graph with 1.3M nodes, 40M edges, and an action log consisting of 35M tuples referring to 300K distinct actions. Beyond showing that there is genuine influence happening in a real social network, we show that our techniques have excellent prediction performance.

/pdf/learning-influence-probabilities-in-social-networks-1cmlboprs4.pdf

Learning influence probabilities in social networks

Innovation is one of the most important issues in business research today. It has been studied in many independent research traditions. Our understanding and study of innovation can benefit from an integrative review of these research traditions. In so doing, we identify 16 topics relevant to marketing science, which we classify under five research fields: - Consumer response to innovation, including attempts to measure consumer innovative-ness, models of new product growth, and recent ideas on network externalities - Organizations and innovation, which are increasingly important as product development becomes more complex and tools more effective but demanding - Market entry strategies, which includes recent research on technology revolution, exten-sive marketing science research on strategies for entry, and issues of portfolio manage-ment - Prescriptive techniques for product development processes, which have been transformed through global pressures, increasingly accurate customer input, web-based communica-tion for dispersed and global product design, and new tools for dealing with complexity over time and across product lines - Defending against market entry and capturing the rewards of innovating, which includes extensive marketing science research on strategies of defense, managing through metrics and rewards to entrants For each topic, we summarize key concepts and highlight research challenges. For pre-scriptive research topics, we also review current thinking and applications. For descriptive top-ics, we review key findings.

Research on Innovation: A Review and Agenda for Marketing Science

We study the problem of maximizing the expected spread of an innovation or behavior within a social network, in the presence of “word-of-mouth” referral. Our work builds on the observation that individuals’ decisions to purchase a product or adopt an innovation are strongly influenced by recommendations from their friends and acquaintances. Understanding and leveraging this influence may thus lead to a much larger spread of the innovation than the traditional view of marketing to individuals in isolation.

In this paper, we define a natural and general model of influence propagation that we term the decreasing cascade model, generalizing models used in the sociology and economics communities. In this model, as in related ones, a behavior spreads in a cascading fashion according to a probabilistic rule, beginning with a set of initially “active” nodes. We study the target set selection problem: we wish to choose a set of individuals to target for initial activation, such that the cascade beginning with this active set is as large as possible in expectation. We show that in the decreasing cascade model, a natural greedy algorithm is a 1-1/ e-e approximation for selecting a target set of size k.

/pdf/influential-nodes-in-a-diffusion-model-for-social-networks-5rikbcbaun.pdf

Influential nodes in a diffusion model for social networks

Aggregate level simulation procedures have been used in many areas of marketing. In this paper we show how individual level simulations may be used support marketing theory development. More specifically, we show how a certain type of simulations that is based on complex systems studies (in this case Stochastic Cellular Automata) may be used to generalize diffusion theory one of the fundamental theories of new product marketing. Cellular Automata models are simulations of global consequences, based on local interactions between individual members of a population, that are widely used in complex system analysis across disciplines. In this study we demonstrate how the Cellular Automata approach can help untangle complex marketing research problems. Specifically, we address two major issues facing current theory of innovation diffusion: The first is general lack of data at the individual level, while the second is the resultant inability of marketing researchers to empirically validate the main assumptions used in the aggregate models of innovation diffusion. Using a computer-based Cellular Automata Diffusion Simulation, we demonstrate how such problems can be overcome. More specifically, we show that relaxing the commonly used assumption of homogeneity in the consumers’ communication behavior is not a barrier to aggregate modeling. Thus we show that notwithstanding some exceptions, the well-known Bass model performs well on aggregate data when the assumption that that all adopters have a possible equal effect on all other potential adopters is relaxed. Through Cellular Automata we are better able to understand how individual level assumptions influence aggregate level parameter values, and learn the strengths and limitations of the aggregate level analysis. We believe that this study can serve as a demonstration towards a much wider use of Cellular Automata models for complex marketing research phenomena.

Using Complex Systems Analysis to Advance Marketing Theory Development: Modeling Heterogeneity Effects on New Product Growth through Stochastic Cellular Automata

The chilling effects of network externalities

Using data on a large number of innovative products in the consumer electronics industry, the authors find that between one-third and one-half of the sales cases involved the following pattern: an initial peak, then a trough of sufficient depth and duration to exclude random fluctuations, and eventually sales levels that exceeded the initial peak. This newly identified pattern, which the authors call a “saddle,” is explained by the dual-market phenomenon that differentiates between early market adopters and main market adopters as two separate markets. If these two segments—the early market and the main market—adopt at different rates, and if this difference is pronounced, then the overall sales to the two markets will exhibit a temporary decline at the intermediate stage. The authors employ both empirical analysis and cellular automata, an individual-level, complex system modeling technique for generating and analyzing data, to investigate the conditions under which a saddle occurs. The model hi...

Riding the Saddle: How Cross-Market Communications Can Create a Major Slump in Sales

https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfiles/3390/BadNewsMarch2007final.pdf

The NPV of bad news

One of the main problems associated with early-period assessment of new product success is the lack of sufficient sales data to enable reliable predictions. We show that managers can use spatial dimension of sales data to obtain a predictive assessment of the success of a new product shortly after launch time.

Based on diffusion theory, we expect that for many innovative products, word of mouth and imitation play a significant role in the success of an innovation. Because word-of-mouth spread is often associated with some level of geographical proximity between the parties involved, one can expect "clusters" of adopters to begin to form. Alternatively, if the market reaction is widespread reluctance to adopt the new product, then the word-of-mouth effect is expected to be significantly smaller, leading to a more uniform pattern of sales assuming that there are no external reasons for clustering. Hence, the less uniform a product's distribution, the higher its likelihood of generating a "contagion process" and therefore of being a success. This is also true if the underlying baseline distribution is nonuniform, as long as it is an empirical distribution known to the firm.

We use a spatial divergence approach based on cross-entropy divergence measures to determine the "distance" between two distribution functions. Using both simulated and real-life data, we find that this approach has been capable of predicting success in the beginning of the adoption process, correctly predicting 14 of 16 actual product introductions in two product categories. We also discuss the limitations of our approach, among them the possible confusion between natural formation of geodemographic clusters and word-of-mouth-based clusters.

/pdf/from-density-to-destiny-using-spatial-dimension-of-sales-426objlx62.pdf

Eitan Muller

Papers

Using Complex Systems Analysis to Advance Marketing Theory Development: Modeling Heterogeneity Effects on New Product Growth through Stochastic Cellular Automata

The chilling effects of network externalities

Riding the Saddle: How Cross-Market Communications Can Create a Major Slump in Sales

The NPV of bad news

From Density to Destiny: Using Spatial Dimension of Sales Data for Early Prediction of New Product Success