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Network (positive) externality describes the phenomenon that when people align their behaviors with others, they can incur an explicit benefit. A good example of network externality is the adoption of new technologies. For example, when companies introduce smartphone to the market, the benefit of smartphone to people is determined by how many people are using it. Network externality has been extensively studied. However, many previous results only focus on the impact of population size on network externality and only capture the influence of population size on people's willingness to adopt to a new technology. They did not consider the effect of heterogeneity, for example, different people can cast different influence on others and also different people can be influenced differently.
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