Here is one such example game: The two players both give a sha1 hash value, then they both give pre-images for their own value. If a player gives an invalid pre-image, they automatically lose. If both players give valid pre-images and the pre-images have the same first bit, the first player wins, otherwise the second player wins. (This isn't a simultaneous move game - I didn't give a move order because the order of reveals doesn't change the game's mechanics any.)
Quite simple from a cryptographic standpoint, but that serves to give us some intuitions for things to avoid in game design - large artifices which you create over time without interference from the opponent, and winning criteria which have to do with a combination of player results rather than a comparison of them.
