Cellular has always relied on static deployments for providing wireless access. However, even the emerging fifth-generation (5G) networks may face difficulty in supporting the increased traffic demand with rigid, fixed infrastructure without substantial over-provisioning. This is particularly true for spontaneous large-scale events that require service providers to augment capacity of their networks quickly. Today, the use of aerial devices equipped with high-rate radio access capabilities has the potential to offer the much needed on-demand capacity boost. Conversely, it also threatens to rattle the long-standing business strategies of wireless operators, especially as the gold rush for cheaper millimeter wave (mmWave) spectrum lowers the market entry barriers. However, the intricate structure of this new market presently remains a mystery. This paper sheds light on competition and cooperation behavior of dissimilar aerial mmWave access suppliers, concurrently employing licensed and license-exempt frequency bands, by modeling it as a vertically differentiated market where customers have varying preferences in price and quality. To understand viable service provider strategies, we begin with constructing the Nash equilibrium for the initial market competition by employing the Bertrand and Cournot games. We then conduct a unique assessment of short-term market dynamics, where two licensed-band service providers may cooperate to improve their competition positions against the unlicensed-band counterpart intruding the market. Our unprecedented analysis studies the effects of various market interactions, price-driven demand evolution, and dynamic profit balance in this novel type of ecosystem.