Rethinking Lock-in and Locking: Adopters Facing Network Effects

When are we locked in a path? This is one of the main questions concerning path dependency. Coming from Arthur's model of increasing returns and technology adoption (Arthur 1989), this paper addresses the question of when and how a lock-in occurs. To gain a better understanding of the path process, different modifications are made. First, the random selection of two types of adopters is substituted with a random selection of adopters having a Gaussian distributed natural inclination. Second, Arthur's model shows only indirect network effects, so direct network effects are added to the model. Furthermore, it is shown that there is an asymptotic lock-in function referring to the technology A and B adopter ratio; this ratio is calculated within the process on the basis of a returning probability to an open state. In the following, the developed model is used to simulate path process without increasing returns, with increasing returns stopping when a lock-in occurs, as well as random drop-outs of increasing returns. One answer that could be drawn out of this new extended model is that there is no lock-in without further stabilizing returns. This and other aspects are used to provide a simplified path-model for empirical research. Finally, its limits are discussed in regard to uncertainty, innovation, and changes in network effect parameters.