On Pure-Strategy Nash Equilibria in a Duopolistic Market Share Model

This paper develops a duopolistic discounted marketing model with linear advertising costs and advertised prices for mature markets still in expansion. Generic and predatory advertising effects are combined together in the model. We characterize a class of advertising models with some lowered production costs. For such a class of models, advertising investments have a no-free-riding strict Nash equilibrium in pure strategies if discount rates are small. We discuss the entity of this efficiency at varying of parameters of our advertising model. We provide a computational framework in which market shares can be computed at equilibrium, too. We analyze market share dynamics for an asymmetrical numerical scenario where one of the two firms is more effective in generic and predatory advertising. Several numerical insights on market share dynamics are obtained. Our computational framework allows for different scenarios in practical applications and it is developed, thanks to Mathematica software.

Market Share Dynamics and the “Persistence of Leadership” Debate

A new 45-industry, 23-year, dataset for Japan is used to investigate the duration of industry leadership. A new scaling relationship linking a firm's current market share with the standard deviation of market share changes is reported. This relationship discriminates in a powerful way between rival candidate theoretical models of market share dynamics. It also makes possible a useful simplification in testing a benchmark model of a Markovian kind. Relative to that model, it is found that at least some industries display a “Chandlerian” bias toward longer durations of leadership than would be present in the benchmark model. (JEL D43, L13)