A Consumer-Based Model of Competitive Diffusion of Two Goods: The Effects of Network Externalities and Local Interactions

The diffusion of two competitive, interchangeable, and durable goods is studied under the framework of a spatial game where consumers are distributed on a two-dimensional square lattice and play 3$\times$3 symmetric coordination-like games with their nearest neighbors. There are three strategies, either consuming a product A or B, or a strategy C of not consuming either A or B. The payoff matrix of the game contains the positive effects of network externality, that is, the payoffs are increasing functions of the number of agents adopting the strategies A or B. Both simulations and mean-field approximation show that the existence of the positive effects of the network externality amplifies any slight initial difference in the number of agents who adopt either A or B and eventually promotes the superior product to take over the entire market. On the other hand, without effects of the network externality the slight initial difference is not enlarged and both superior and inferior products are observed to coexist by forming clusters in the market. Moreover, the effects of innovation factors that help an inferior product to retake the market are studied. It is shown that both the timing and size of the innovation factor matter for an inferior product in order to retake the market.competitive diffusion, network externality, local interaction, global externality, local externality, evolutionary game, spatial game

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. Copyright Springer-Verlag Berlin/Heidelberg 2005Competitive diffusion, Technological Standardization, Global and local network externalities, Spatial coordination game, Dynamic payoffs,