Inverted-U aggregate investment curves in a dynamic game of advertising

•We examine firms' investments in brand equity in a differential game with product differentiation.•The feedback equilibrium obtains under open-loop rules.•Aggregate expenditure takes an inverted-U shape under both Cournot and Bertrand behaviour if differentiation is high.•Total industry expenditure is higher under Cournot competition.

We revisit the relationship between market power and firms' investment incentives in a noncooperative differential oligopoly game where firms sell differentiated goods and invest in advertising to increase the brand equity of their respective goods. The feedback equilibrium obtains under open-loop rules, and aggregate expenditure on goodwill takes an inverted-U shape under both Cournot and Bertrand behaviour, provided product differentiation is sufficiently high. Total industry expenditure is higher under Cournot competition.