Well, this is especially bad. F1's marketing clout just isn't strong enough for even someone like Bridgestone, the eminent worldwide high perf tire mfr.
I'm guessing this will simmer and there will be a new deal with money going to Bridgestone from the teams, in the form of higher tire prices. I don't see any other company with big enough shoes to fill this gap, except for Michelin, and that company has a long history of flighty involvement in racing.
Bridgestone already has infrastructure in place. They are the logical ones to choose. Bernie is going to have to readjust his "rape and pillage" method of F1 sponsorship deals.