We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses neighbours by preferential attachment, and selects its type based on the number of initial neighbours of each type. The model is analysed in detail, and in particular, we determine the possible proportions of the various types in the limit of large networks. An important qualitative feature we find is that, in contrast to many current theoretical models, often several competitors will coexist. This matches empirical observations in many real-world networks.
In marketing, competing companies fight for customers. In essence, our model describes word-of-mouth recommendations, and thus it should be compared to other models which study the effect of such personal recommendations. A related model of word-of-mouth learning was studied by Banerjee and Fudenberg @cite_32 , where successive generations of agents make choices between two alternatives, with new agents sampling the choices of old ones. However, they considered the limit of a continuum of agents with no network structure, in contrast to our setup, where this is explicitly modeled. Furthermore, they assume that one of the two alternatives is ex-ante better'' than the other, and focus on whether or not the agents can learn this via word-of-mouth communication. See also @cite_17 @cite_15 .
@cite_15 @cite_32 @cite_17
2115926002 2122489728 1654194294 2105509646
This paper analyzes a model of rational word-of-mouth learning, in which successive generations of agents make once-and-for-all choices between two alternatives. Before making a decision, each new agent samples N old ones and asks them which choice they used and how satisfied they were with it. If (a) the sampling rule is “unbiased” in the sense that the samples are representative of the overall population, (b) each player samples two or more others, and (c) there is any information at all in the payoff observations, then in the long run every agent will choose the same thing. If in addition the payoff observation is sufficiently informative, the long-run outcome is efficient. We also investigate a range of biased sampling rules, such as those that over-represent popular or successful choices, and determine which ones favor global convergence towards efficiency. This paper studies the way that word-of-mouth communication aggregates the information of individual agents. We find that the structure of the communication process determines whether all agents end up making identical choices, with less communication making this conformity more likely. Despite the players' naive decision rules and the stochastic decision environment, word-of-mouth communication may lead all players to adopt the action that is on average superior. These socially efficient outcomes tend to occur when each agent samples only a few others. 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. We consider the problem faced by a company that wants to use viral marketing to introduce a new product into a market where a competing product is already being introduced. We assume that consumers will use only one of the two products and will influence their friends in their decision of which product to use. We propose two models for the spread of influence of competing technologies through a social network and consider the influence maximization problem from the follower's perspective. In particular we assume the follower has a fixed budget available that can be used to target a subset of consumers and show that, although it is NP-hard to select the most influential subset to target, it is possible to give an efficient algorithm that is within 63 of optimal. Our computational experiments show that by using knowledge of the social network and the set of consumers targeted by the competitor, the follower may in fact capture a majority of the market by targeting a relatively small set of the right consumers.