A consumer-based model of competitive diffusion: the multiplicative effects of global and local network externalities

Competitive diffusion of two incompatible technologies, such as PC vs. Macintosh, VHS vs. Betamax and so on, is studied under the framework of a spatial game in which consumers are distributed on a two-dimensional square lattice network. The consumers play coordination-like games with their nearest neighbors and imitate the most successful strategy in their neighborhood in terms of aggregated payoffs after each round. The effects of global network externality are realized in the dynamic payoff matrix of the game, and the framework of spatial game provides the model with the effects of local network externality. These two types of externalities are set as multiplicative, that is, as nonlinear. Both simulations and mean-field approximation show that not only total but also partial standardization (robust polymorphic equilibrium) occurs depending upon the parameters and initial configurations, even when there are positive effects of both global and local network externalities. Moreover, effects of innovation factors that alter paths toward a lock-in situation are studied. It is shown that both the timing and the size of the innovation factors matter for a disadvantaged technology in order to overwhelm a market.