Recent advances in communications and IT technology have underpinned the rapid development of trans- portation network companies (TNCs) in recent years. Although the competitive prices offered by TNCs have been well-received by users, recent studies indicate that the resulting increase in public welfare  is temporary, as passengers are likely to be steered away from public transport. Indeed, a recent study by has presented evidence that such shifts have already occurred and can be directly linked to increased congestion in major cities. Many studies in taxi pricing have adopted an economic theory perspective, using aggregate demand and supply models to represent the dynamics of urban taxi operations. However, the relationship between dynamic TNC pricing strategies and public transport provision remains unexplored to this date. To address this issue, we propose a novel, game-theoretic, dynamic pricing model that accounts for multiple TNCs operating alongside public transport services. This is applied to a city-wide service scenario, and compared to an alternative static pricing model that serves as a baseline. Finally, we perform a comparative analysis of expected utilities for travellers and operators, while monitoring mode share fluctuations across a range of competitive scenarios and market structures.