An infinite horizon differential game of optimal CLV-based strategies with non-atomic firms

We study optimal customer acquisition and retention strategies in an infinite-horizon model of dynamic competition. We find that acquisition expenditures constitute the larger share of the marketing budget, when the customer profit margin is either low or large, but for intermediate profit margin values, firms spend more resources for customer retention. If customer profit margins rise for exogenous reasons, we find that the share of customer acquisition expenditures in the marketing budget increases in markets with high profit margins, whereas it decreases in markets with low profit margins. The impact of entry of new firms in the market on the optimal strategy depends on the effect of the entry on profit margins and absolute levels of profit margins. A similar phenomenon may also appear in a single segmented market: the impact of higher competition on the luxury and mass- consumption segments of a market would be different.