Doesn't Binance and other exchange host these kind of competition although I am not that familiar with it though. I would like to see a competition that's being livestreamed because it seems like the price prediction competition is definitely going to be intense if you ask me especially if the competitors aren't professional traders.
They all do but it seems the OP isn't aware. The first service providers I knew offer such contest were exchange. A quick search on Google and you'll finds hundreds of such prediction contest, coinmarketcap has also joined same as other projects hoping to get some attention to their platform. Wallet service providers also do rhis. Basically majority of the service providers engage in this contest as it's one of the most easiest way to get enthusiast into knowing about your project.
Next to airdropping of tokens to get new users attention and publicity, we have organizing prediction or trading contest. The contest is also organized on the forum especially on the speculation board. Just keep your eyes there and you might come in contact with one although there's usually some criteria you have to meet before you can participate. Also we have gambling platform giving the forum users an opportunity to earn some funds via prediction contest they carry out on game and rounds subboard via the gambling board.