The Hope Video is an item featured in Danganronpa 3: The End of Hope's Peak Academy. It was created by Ryota Mitarai to brainwash the entire world into believing in Hope, consequently removing all despair that has been caused by the previous video that Ryota unwittingly created, the Despair Video.
The video itself appears to have a bright symmetrical pattern, similar to what one would see in a kaleidoscope. When someone watches such video, their eyes shine a similarly bright color, forcefully making them believe in hope and erasing any trace of despair from their minds.
The Hope Video was created some time before the Final Killing Game. Kazuo Tengan, shortly after receiving the direct antagonist to the Hope Video and a video of the Student Council Killing Game from Chisa Yukizome, began planning the Final Killing Game in order for Ryota to be given the final push to broadcast his video all around the world.
However, the aforementioned plan was stymied by the fact Ryota became a participant of the Final Killing Game when he wasn't supposed to be, with his NG Code forbidding him to use his talent at all. As such, he was unable to make use of the Hope Video for the entirety of the event until Juzo Sakakura switched off the bangles' power and ended the killing game.
As soon as this happened, Ryota resolved to broadcast his Hope Video around the world all according to Kazuo's plan. After brainwashing Aoi Asahina in order for her to distract Makoto Naegi and preventing him from stopping his plans, and doing the same to the Future Foundation's rescue squad to give himself extra safety in the execution of his plans, he made his way towards the broadcasting studio and began uploading the Hope Video worldwide, this process taking 30 minutes before full completion.
In spite of this, the former Remnants of Despair, awakening from their coma thanks to Izuru Kamukura, swiftly defeated Future Foundation's task force and faced Ryota. After managing to convince him to stop his broadcasting, he effectively stopped it moments before full completion. Nonetheless, the brief broadcast of his Hope Video was sufficient to erase all traces of despair in the world.