A Diagnostic for Lock-In

In the context of increasing returns markets, the conventional argument is that a slender market share advantage may entrain a firm on a trajectory bound for monopoly in the long run. We revisit this with the linear urn model representation of history dependence, and a probabilistic characterization of eventual dominance. It is possible to explore the implications of varying the strength of feedback with a simple Pólya-urn scheme. It is then possible to determine how much stronger the positive feedback needs to be, in order to compensate for smaller initial market share of a firm, in attaining any specified degree of dominance. This allows us to place bounds on the probability that a firm will come to dominate an increasing returns market in the long run