Spillover Effects, Adaptive Learning And Long Run Market Shares

We consider the impact of local and global spillover effects on the long run market shares of two populations of firms (e.g.~firms based in two different regions) who compete on a high-tech market. Production costs of a firm are (strongly) influenced by the number of local firms and (weakly) by the number of foreign firms in the market. Every period firms in both populations decide whether to exit or enter the market based on information about the profitability of the market compared to an outside option. This information which is spread through Word-of-Mouth communication is noisy. Equilibria and basins of attraction of the resulting market share dynamics are analyzed using the concepts of critical curves. We demonstrate under which conditions the market is entirely taken over by firms from one single population and in how far the long run otucome depends on the initial market shares. The set of initial market conditions where such market takeovers occur neither depends continuously on the parameters of the model nor is a connected set. Rather the size of the basins of attraction of these steady states changes abruptly due to basin bifurcations and might develop into a complex non-connected structure. The characterization of such transitions of the basins of attraction for several parameter variations allows interesting insights into the question which factors are crucial for a population to be able to take over the market. In particular, it is also shown that often improving the ability to import know-how from the other population is more helpful for a market takeover than increasing local spillover effects.