(glancing around in mild bemusement)
Seriously, people. Where do you think we even got the word "sponsor" from?
In its original usage it meant a guarantor: someone who promised you that you were going to get something out of what they were doing.
Throwing a ludus / game or a series of games was expensive. Local (or national) Roman politicians put down good money to pay for the rental of the event space (you think the Colosseum was cheap to rent? Think again. The Imperials who built it liked to make their money back...), the wages (and overtime!) of the hundreds of venue support staff, the fees required by the fighting talent and the schools that owned them (or their own management, if they were free), and so forth.
Whoever was footing the bill for a given Game (or sequence of Games) was formally known by the title sponsor, and got to parade around the arena at the beginning of the game to remind people in the stands just who was fulfilling their civic duty by throwing this entertainment for them. The message was, "I'm doing something for you. Next election, don't forget to do something for me!"
And it was always political. Never lose sight of that. (Especially when a local political party promises to build you a nice new stadium if you elect them. The more some things change, the more they stay the same...)
(cc: @petermorwood) 😏