In simple terms, both superpowers poured gasoline on the fire and fanned the flames, hoping that out of the ashes would arise a region committed either to democracy or to Soviet-style communism.

Far from putting a distance between them, his absence was only fanning the flames of her affection.

They worried, too, that such a war would only fan the flames of the Islamic world's animosity toward the United States, producing "a further cycle of terrorist attacks, American casualties and escalation" […]

Atlanta newspapers fanned the flames of racial hatred by carrying stories of lynchings and calling for a renewed Ku Klux Klan to “control” blacks.

What I don't see happening is the government fanning the flames of competition.

Fan the flames

Meaning

Verb