In Battle B-Daman, the IBA is the worldwide sanctioning body for B-Daman in the B-DaWorld, hosting tournaments and events throughout. Every year, they host their biggest tournament, the IBA Winners Tournament.
The JBA, again is the sanctioning body for B-Daman. They promote peace through the sport of B-Daman, that which drew contempt from the Saionji Konzern as a matter of principle, since the latter creates destructive weaponry. The JBA also host the B-1 Crash Cup.
In Real Life
The B-Daman sactioning body is just Takara-Tomy (Takara at the time) hosting B-Daman tournaments and events in real life, sometimes with help from CoroCoro Comic. The logo, or at least the initials, can be found on certain B-Daman products.