This thesis seeks to contribute to the emerging body of theoretical research uniting the literature of new growth theory with that of dynamic oligopoly, modeled by differential games. A differential game theoretic model of duopoly by Sorger (1989) is first extended into a partial equilibrium model of macroeconomic growth with duopolistic competition in production. Firms in the single, duopolistic production sector compete for market share by investing in quality improvement of the consumption good produced, adopting feedback Nash Equilibrium strategies. Since labour is assumed to be the only input into quality improving activities, a solution for steady state economic growth is obtained by endogenising the labour market. The model is then extended to a partial equilibrium growth model with N firm oligopolistic competition in production. Finally, the model is inserted into a dynamic general equilibrium framework by introducing utility maximising consumers. It is assumed that firms in the single, oligopolistic production sector earn zero economic profits, such that an endogenous solution for the number of firms in the economy is derived. Both the interest rate and the wage rate are endogenised in order to establish the conditions under which steady state growth will occur. It is found that there is a trade off between economic growth and the competitiveness of the production sector. This is because as the economy approaches perfect competition (i.e. the number of firms in production becomes large) the returns to each firm from quality improvement decline. Consequently, the amount of quality improving activities performed by firms declines, as does economic growth.