This paper provides an examination of an oligopoly market for addictive commodities, specifically cigarettes. The model is characterized by overlapping generations of consumers and differentiated products. A price equilibrium, which is both stationary and symmetric, is characterized. The model accounts for many of the features within the South African tobacco market. Although excise taxes rose in South Africa, and the actual price in the market rose by more than the increase in the excise tax, the model shows that the increase in the price beyond the excise tax was caused by factors other than the change in the tax rate. The model also points to potential empirical problems associated with estimating cigarette market outcomes, due to the fact that the combination of market structure and addiction may greatly impact the assumed exogeneity of the prices used in the analysis.