Game Theoretic Analysis of a Strategic Model of Competitive Contagion and Product Adoption in Social Networks

In this paper we propose and study a strategic model of marketing and product adoption in social networks. Two firms compete for the spread of their products in a social network. Considering their fixed budgets, they initially determine the payoff of their products and the number of their initial seeds in a network. Afterwards, neighboring agents play a local coordination game over a fixed network which determines the dynamics of the spreading. Assuming myopic best response dynamics, agents choose a product based on the payoff received by actions of their neighbors. This local update dynamics results in a game-theoretic diffusion process in the network. Utilizing earlier results in the literature, we find a lower and an upper bound on the proportion of product adoptions. We derive an explicit characterization of these bounds based on the payoff of products offered by firms, the initial number of adoptions and the underlying structure of the network. We then consider a case in which after switching to the new product, agents might later switch back to the old product with some fixed rate. We show that depending on the rate of switching back to the old product, the new product might always die out in the network eventually. Finally, we consider a game between two firms aiming to optimize their products adoptions while considering their fixed budgets. We describe the Nash equilibrium of this game and show how the optimal payoffs offered by firms and the initial number of seeds depend on the relative budgets of firms

Modeling Adoption and Usage of Competing Products

The emergence and wide-spread use of online social networks has led to a dramatic increase on the availability of social activity data. Importantly, this data can be exploited to investigate, at a microscopic level, some of the problems that have captured the attention of economists, marketers and sociologists for decades, such as, e.g., product adoption, usage and competition. In this paper, we propose a continuous-time probabilistic model, based on temporal point processes, for the adoption and frequency of use of competing products, where the frequency of use of one product can be modulated by those of others. This model allows us to efficiently simulate the adoption and recurrent usages of competing products, and generate traces in which we can easily recognize the effect of social influence, recency and competition. We then develop an inference method to efficiently fit the model parameters by solving a convex program. The problem decouples into a collection of smaller subproblems, thus scaling easily to networks with hundred of thousands of nodes. We validate our model over synthetic and real diffusion data gathered from Twitter, and show that the proposed model does not only provides a good fit to the data and more accurate predictions than alternatives but also provides interpretable model parameters, which allow us to gain insights into some of the factors driving product adoption and frequency of use

Hipsters on Networks: How a Small Group of Individuals Can Lead to an Anti-Establishment Majority

The spread of opinions, memes, diseases, and "alternative facts" in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread. In this paper, we explore how \textit{anti-establishment} nodes (e.g., \textit{hipsters}) influence the spreading dynamics of two competing products. We consider a model in which spreading follows a deterministic rule for updating node states (which describe which product has been adopted) in which an adjustable fraction $p_{\rm Hip}$ of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two. The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted. We simulate our model on both synthetic and real networks, and we show that the hipsters have a major effect on the final fraction of people who adopt each product: even when only one of the two products exists at the beginning of the simulations, a very small fraction of hipsters in a network can still cause the other product to eventually become the more popular one. To account for this behavior, we construct an approximation for the steady-state adoption fraction on $k$-regular trees in the limit of few hipsters. Additionally, our simulations demonstrate that a time delay $\tau$ in the knowledge of the product distribution in a population, as compared to immediate knowledge of product adoption among nearest neighbors, can have a large effect on the final distribution of product adoptions. Our simple model and analysis may help shed light on the road to success for anti-establishment choices in elections, as such success can arise rather generically in our model from a small number of anti-establishment individuals and ordinary processes of social influence on normal individuals.Comment: Extensively revised, with much new analysis and numerics The abstract on arXiv is a shortened version of the full abstract because of space limit

Adoption as a Social Marker: Innovation Diffusion with Outgroup Aversion

Social identities are among the key factors driving behavior in complex societies. Signals of social identity are known to influence individual behaviors in the adoption of innovations. Yet the population-level consequences of identity signaling on the diffusion of innovations are largely unknown. Here we use both analytical and agent-based modeling to consider the spread of a beneficial innovation in a structured population in which there exist two groups who are averse to being mistaken for each other. We investigate the dynamics of adoption and consider the role of structural factors such as demographic skew and communication scale on population-level outcomes. We find that outgroup aversion can lead to adoption being delayed or suppressed in one group, and that population-wide underadoption is common. Comparing the two models, we find that differential adoption can arise due to structural constraints on information flow even in the absence of intrinsic between-group differences in adoption rates. Further, we find that patterns of polarization in adoption at both local and global scales depend on the details of demographic organization and the scale of communication. This research has particular relevance to widely beneficial but identity-relevant products and behaviors, such as green technologies, where overall levels of adoption determine the positive benefits that accrue to society at large.Comment: 26 pages, 10 figure

Identifying influencers in a social network : the value of real referral data

Individuals influence each other through social interactions and marketers aim to leverage this interpersonal influence to attract new customers. It still remains a challenge to identify those customers in a social network that have the most influence on their social connections. A common approach to the influence maximization problem is to simulate influence cascades through the network based on the existence of links in the network using diffusion models. Our study contributes to the literature by evaluating these principles using real-life referral behaviour data. A new ranking metric, called Referral Rank, is introduced that builds on the game theoretic concept of the Shapley value for assigning each individual in the network a value that reflects the likelihood of referring new customers. We also explore whether these methods can be further improved by looking beyond the one-hop neighbourhood of the influencers. Experiments on a large telecommunication data set and referral data set demonstrate that using traditional simulation based methods to identify influencers in a social network can lead to suboptimal decisions as the results overestimate actual referral cascades. We also find that looking at the influence of the two-hop neighbours of the customers improves the influence spread and product adoption. Our findings suggest that companies can take two actions to improve their decision support system for identifying influential customers: (1) improve the data by incorporating data that reflects the actual referral behaviour of the customers or (2) extend the method by looking at the influence of the connections in the two-hop neighbourhood of the customers

Diffusion of shared goods in consumer coalitions. An agent-based model

This paper focuses on the process of coalition formation conditioning the common decision to adopt a shared good, which cannot be afforded by an average single consumer and whose use cannot be exhausted by any single consumer. An agent based model is developed to study the interplay between these two processes: coalition formation and diffusion of shared goods. Coalition formation is modelled in an evolutionary game theoretic setting, while adoption uses elements from both the Bass and the threshold models. Coalitions formation sets the conditions for adoption, while diffusion influences the consequent formation of coalitions. Results show that both coalitions and diffusion are subject to network effects and have an impact on the information flow though the population of consumers. Large coalitions are preferred over small ones since individual cost is lower, although it increases if higher quantities are purchased collectively. The paper concludes by connecting the model conceptualisation to the on-going discussion of diffusion of sustainable goods, discussing related policy implications