تاثیر بازاریابی بر پخش در شبکه های اجتماعی Marketing impact on diffusion in social networks

1. Introduction 1.1. Social Networks In this article we study how diffusion in social networks could be affected by marketing. Diffusion happens when a product or a social norm is initially adopted by a small group of agents who later influence their peers to adopt the same product. The peers influence their peers, and so on. There are two most commonly used models of diffusion: the cascading model and the threshold model. In the cascading model [18, 12] the behaviour of agents is random and the peer influence manifests itself in a change of a probability of an agent to adopt the product. In the threshold model [24, 14, 11, 1], originally introduced by Granovetter [10] and Schelling [19], the behavior of the agents is deterministic. Other models of diffusion, such as propositional opinion diffusion model [9], have also been studied. The focus of this article is on the threshold model of diffusion of a given product. In this model, there is a threshold value θ(a) associated with each agent a and an influence value w(a, b) associated with each pair of agents a and b. Informally, the threshold value θ(a) represents the resistance of agent a to adoption of the product and the influence value w(a, b) represents the peer pressure that agent a puts on agent b upon adopting the product. If the total peer pressure from the set of agents A who have already adopted the product on an agent b is no less than the threshold value θ(b), i.e.,  then agent b also adopts the product. 1.2. Influence Relation We say that a set of agents A influences a set of agents B if the social network is such that an adoption of the product by all agents in set A will unavoidably lead to an adoption of the product by all agents in set B. Note that it is not important how original adoption of the product by agents in set A happens. For example, agents in set A can receive and start using free samples of the product. Also, agents in set A can influence agents in set B indirectly. If agents in set A put enough peer pressure on some other agents to adopt the product, who in turn put enough peer pressure on the agents in set B to adopt the product, we still say that set A influences set B. We denote this influence relation by A B.