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
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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 give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree distributions and, more generally, the limiting distribution of subgraphs in balls of any given radius @math around a random vertex in the preferential attachment graph. We also establish the finite-volume corrections which give the approach to the limit. This paper studies agents who consider the experiences of their neighbors in deciding which of two technologies to use. We analyze two learning environments, one in which the same technology is optimal for all players and another in which each technology is better for some of them. In both environments, players use exogenously specified rules of thumb that ignore historical data but may incorporate a tendency to use the more popular technology. In some cases these naive rules can lead to fairly efficient decisions in the long run, but adjustment can be slow when a superior technology is first introduced.