The competition of user networks: ergodicity, lock-ins, and metastability

Abstract

This paper models the competition of user networks as a continuous-time Markov process. It presents a dynamic version of the Discrete Choice Analysis with state-dependent choice probabilities. Among other things, we show that the network competition can be characterized by the coexistence of lock-in regimes and a ‘metastable’ state — i.e. a state which is a probability maximum for an arbitrary long but finite length of time. Then, unlike in the case of ergodicity or of simple lock-in scenarios, the networks can coexist for a considerable time span, although the market is a natural monopoly.