How to Influence People with Partial Incentives

We study the power of fractional allocations of resources to maximize influence in a network. This work extends in a natural way the well-studied model by Kempe, Kleinberg, and Tardos (2003), where a designer selects a (small) seed set of nodes in a social network to influence directly, this influence cascades when other nodes reach certain thresholds of neighbor influence, and the goal is to maximize the final number of influenced nodes. Despite extensive study from both practical and theoretical viewpoints, this model limits the designer to a binary choice for each node, with no way to apply intermediate levels of influence. This model captures some settings precisely, e.g. exposure to an idea or pathogen, but it fails to capture very relevant concerns in others, for example, a manufacturer promoting a new product by distributing five "20% off" coupons instead of giving away one free product. While fractional versions of problems tend to be easier to solve than integral versions, for influence maximization, we show that the two versions have essentially the same computational complexity. On the other hand, the two versions can have vastly different solutions: the added flexibility of fractional allocation can lead to significantly improved influence. Our main theoretical contribution is to show how to adapt the major positive results from the integral case to the fractional case. Specifically, Mossel and Roch (2006) used the submodularity of influence to obtain their integral results; we introduce a new notion of continuous submodularity, and use this to obtain matching fractional results. We conclude that we can achieve the same greedy $(1-1/e-\epsilon)$-approximation for the fractional case as the integral case. In practice, we find that the fractional model performs substantially better than the integral model, according to simulations on real-world social network data

INFLUENCE MAXIMIZATION IN SOCIAL NETWORKS

In the social network era, every decision an individual makes, whether it is watching a movie or purchasing a book, is influenced by his or her personal network to a certain degree. This thesis investigates the power of the “word-of-mouth” effect within social networks. Given a network G = (V, E, t) where t(v) denotes the threshold of node v, we model the spread of influence as follows. Influence propagates deterministically in discrete steps. An influenced node u exerts a fixed amount of influence bu,w on any neighbor w. For any uninfluenced node v, if the total amount of influence it receives from all its already influenced neighbors at time step t− 1 is at least t(v), node v will be influenced in step t. Given a social network G, we study the problem of introducing an already activated external influencer v into the network, and choosing links from v to nodes in G that can maximize the spread of influence in G. We study two problems: the Minimum Links problem, which is to choose the minimum number of links that can activate the entire network, and the Maximum Influence problem, which is to choose k neighbors that will maximize the size of the influenced set. We prove that the Maximum Influence problem is NP-hard, even for bipartite graphs in which thresholds of all nodes are either one or two. We also study both problems in paths, rings, trees and cliques, and we give polynomial time algorithms that find optimal solutions to both problems for all these topologies

Social Media Influencers- A Review of Operations Management Literature

This literature review provides a comprehensive survey of research on Social Media Influencers (SMIs) across the fields of SMIs in marketing, seeding strategies, influence maximization and applications of SMIs in society. Specifically, we focus on examining the methods employed by researchers to reach their conclusions. Through our analysis, we identify opportunities for future research that align with emerging areas and unexplored territories related to theory, context, and methodology. This approach offers a fresh perspective on existing research, paving the way for more effective and impactful studies in the future. Additionally, gaining a deeper understanding of the underlying principles and methodologies of these concepts enables more informed decision-making when implementing these strategie

Computational Analysis of Intelligent Agents: Social and Strategic Settings

The central motif of this work is prediction and optimization in presence of multiple interacting intelligent agents. We use the phrase `intelligent agents' to imply in some sense, a `bounded rationality', the exact meaning of which varies depending on the setting. Our agents may not be `rational' in the classical game theoretic sense, in that they don't always optimize a global objective. Rather, they rely on heuristics, as is natural for human agents or even software agents operating in the real-world. Within this broad framework we study the problem of influence maximization in social networks where behavior of agents is myopic, but complication stems from the structure of interaction networks. In this setting, we generalize two well-known models and give new algorithms and hardness results for our models. Then we move on to models where the agents reason strategically but are faced with considerable uncertainty. For such games, we give a new solution concept and analyze a real-world game using out techniques. Finally, the richest model we consider is that of Network Cournot Competition which deals with strategic resource allocation in hypergraphs, where agents reason strategically and their interaction is specified indirectly via player's utility functions. For this model, we give the first equilibrium computability results. In all of the above problems, we assume that payoffs for the agents are known. However, for real-world games, getting the payoffs can be quite challenging. To this end, we also study the inverse problem of inferring payoffs, given game history. We propose and evaluate a data analytic framework and we show that it is fast and performant

Integrating social network effects in the share-of-choice problem

Accounting for social network effects in marketing strategies has become an important issue. Taking a step back, we seek to incorporate and analyze social network effects on new product development and then propose a model to engineer product diffusion over a social network. We build upon the share-of-choice (SOC) problem, which is a strategic combinatorial optimization problem used commonly as one of the methods to analyze conjoint analysis data by marketers in order to identify a product with largest market share, and show how to incorporate social network effects in the SOC problem. We construct a genetic algorithm to solve this computationally challenging (NP-Hard) problem and show that ignoring social network effects in the design phase results in a significantly lower market share for a product. In this setting, we introduce the secondary operational problem of determining the least expensive way of influencing individuals and strengthening product diffusion over a social network. This secondary problem is of independent interest, as it addresses contagion models and the issue of intervening in diffusion over a social network, which are of significant interest in marketing and epidemiological settings

Integrating social network effects in the share-of-choice problem

Accounting for social network effects in marketing strategies has become an important issue. Taking a step back, we seek to incorporate and analyze social network effects on new product development and then propose a model to engineer product diffusion over a social network. We build upon the share-of-choice (SOC) problem, which is a strategic combinatorial optimization problem used commonly as one of the methods to analyze conjoint analysis data by marketers in order to identify a product with largest market share, and show how to incorporate social network effects in the SOC problem. We construct a genetic algorithm to solve this computationally challenging (NP-Hard) problem and show that ignoring social network effects in the design phase results in a significantly lower market share for a product. In this setting, we introduce the secondary operational problem of determining the least expensive way of influencing individuals and strengthening product diffusion over a social network. This secondary problem is of independent interest, as it addresses contagion models and the issue of intervening in diffusion over a social network, which are of significant interest in marketing and epidemiological settings