Market-share analysis focuses on the competitive interrelations between products or brands. Marketing activity may affect the performance of a company's own product and that of its competitors not only within a single time horizon but also over several extended periods. Starting from a static market-share analysis model, the dynamic relationships of market shares between competitive brands are described by multiplicative competitive interaction (MCI) time-series models, in which the problem of logical consistency for estimated shares is resolved. A Bayesian shrinkage estimator solution is applied to the further problem of model-induced collinearity in cross-differential MCI models. Dynamic elasticity is defined and used to measure the delayed and long-term effects of marketing mix variables on market shares. The dynamic relationships of future market shares are predicted by means of predictive density. Strategic simulations are conducted under several scenarios for marketing planning. It is argued that the new dynamic model proposed here, applied to daily national or store tracking data, provides useful insights into dynamic competitive relationships in the marketplace, to the benefit of corporate planners, marketing directors, brand managers and retail strategists.