Spread of smartphones in a network
https://www.technologyreview.com/s/427787/are-smart-phones-spreading-faster-than-any-technology-in-human-history/
Smart phones with touch screens appeared in 1993 and spread to almost half of the population in U.S. in 10 years while other technologies such as telephone or electricity need more than 50 years. Although we can’t say that smartphones always spread faster than any other technology did because the article doesn’t provide enough data, what we can say is that it took less time to spread to half of the population in U.S. The fast spread of smart phones can be expressed by networks and information cascade.
So why did smartphones spread so quickly? Let’s compare it with the spread of electricity which took almost 50 years to spread to half of the population in U.S. Assume the payoff of using electricity is 1. As the technology developed, the cost of using electricity decreased so payoff increased. More people started using electricity.
For smartphones, let’s also assume the payoff is 1 at the beginning, but what makes the spread of smartphone faster than electricity is that, as more people start using smartphones, the payoff gets larger. If a person doesn’t have any friend who uses smartphone, then the payoff for him is probably very low because he can’t call his friends, but if everyone around him uses smartphone, his payoff is a lot higher.
According to the Threshold Rule, people will choose to use smartphone if the fraction of neighbors using it is larger than a threshold q. As payoff increases, threshold q decreases, so the number of people using smartphone increases rapidly.