Geoff recently posted on gentrification. One thing not clear to me lies in whether rising costs of living or immigration cause the problems we see with gentrification.
I guess that most arise from the influx of "foreigners" that trigger social stress, as rising costs force a relocation trend away from the commerce centers, however this occurs within a community that remains more whole than when challenged by immigration (granted, no numbers whatsoever here, just me thinking about how humans cope with different kinds of change, and what support they have).
When the community has control of its laws/land use zoning, it can try to disincent "foreigners" by banning culturally identified land use(ban cars from the district, ban shops of certain types, etc.).
When the community has tax authority, it can establish a substantial progressive income and wealth tax to disincent richer bidders for land occupation.
When a community has neither taxation nor land control, it should have almost zero influence, barring fear/hate campaigns against the immigrants.
This last alternative means either some form of war or welcoming outsiders and somehow transmitting culture with a good enough level of fidelity. Perhaps a particularly aggressive welcoming party that doesn't stop until satisfied?