Soda taxes are commonly used to reduce sugar consumption. The effects of taxes on prices and consumption have been widely studied, however there is less work on the impact of taxes on firms' strategic choices over advertising spending. We study how soda taxes affect both pricing and advertising strategies of firms in a dynamic oligopoly game. We use rich longitudinal data to estimate an equilibrium model of the cola market. We exploit an institutional feature of the advertising market that involves cola firms delegating decisions over advertising spots to agencies. This allows us to model the rich impacts of advertising on demand, while solving the otherwise intractable dynamic equilibrium impact of the introduction of a tax. We find that the dynamic competition game between the main players (Coca Cola and Pepsi) results in asymmetric responses in advertising spending, with both firms reducing advertising expenditure in response to a sugary soda tax.