This isn't an actual game, but I'm thinking it would be great to pick a card face up that's "red" and be able to make a decision to turn it into "cyan". Others could pick "green" and "blue" face up, but can click a button to turn it to something else, and then the game resolves itself when everyone reveals it. Like if everyone can discuss and if everyone reveals the primary colors everyone wins.
I'm sure there's interesting game mechanics you can come up with when you give a decision to the player.
Additionally, I think this could make an interesting programmable suite of games. You don't have to sell just one game.