Both yes and no. For smaller cities, Hyatt probably has some agreement that there can only be one per city, but there are examples of multiple.

Park Hyatt

• London (Park Hyatt London River Thames, Park Hyatt Trafalgar Square (canceled))
• Seoul (another one was announced north of the Han River, while the current one is in Gangnam)

Perhaps Hyatt is lenient as long as theres some sort of body of water separating them.

Andaz

• Shanghai (Andaz Xintiandi, Andaz Shanghai ITC opening next year)
• New York (Andaz 5th Avenue, Hyatt Centric Wall Street (ne้ Andaz))

Grand Hyatt

• Shangai (Grand Hyatt Shanghai, Hyatt on the Bund) If you stay at the Hyatt on the Bund, its considered a Grand Hyatt for brand purposes, and is listed as a Grand Hyatt under locations.

So in summation, Hyatt probably has non compete agreements, but there are exceptions for big cities.