What about them?

Shinkenchiku Residential Design Competition

One of the greatest and most reputable architecture competitions in the world.
And it has been around for ages.
What are the ingredients: every year one starchitect (and we're talking Pritzkers here: Koolhaas, Nishizawa, etc) proposes an idea competition theme (and the themes are very provocative and open-ended: A house with no style, A house with resale value, 9 square grids house, etc) and is the sole juror for the submissions. Submissions are one panel only (hard-copy till few years ago, now entirely digital), the total prize value is around 15.000 euros and the winners get published in the prestigious magazine The Japan Architect. It's a high quality competition, with superb submissions and stimulating feedback from the jury. Plus, if you win the Shinkenchiku competition, you'll probably be hired in any big architecture studio in the world.
There are some drawbacks, of course: there isn't an online/offline archive; the winning submissions are published in thumbnail size on the last pages of the magazine, so often it is impossible to understand them; the feedback from the jury is addressed only to the winners (together with the honorable mentions, they amount around 2% of the total entries). The money prize is of high value but I think that this is not the main drive for anyone entering the competition. It's more like ancient olympics with Zeus paying his respect to the winners.
What to learn from this?
Immense value puts the money in the background.
Still. it's not a business. Just the editor of the magazine is sponsoring a competition. Needs further thinking.

Central Glass International Competition

Quite the same model, except that there is a 7 person jury (still very reputable japanese architects) and the money prize is a lot bigger: around 25.000 euros + travel expenses to Japan for the winners. Probably because this time the sponsor is a company manufacturing architectural glass. And they managed to secure an online archive, which is a real gem.
And yet, it feels that the Shinkenchiku residential competition is the top one. Probably because of the Zeus.

Not a real business, but it works like this: Sponsors Competition.
And it has a western follower, International Velux Award, also with a big name jury, great prizes (30.000 euros) but with a slightly less inspiring brief (it's all about the light!).