They don't really offer discounts. Sometimes they offer incentives if a particular trip/date isn't booking well. The incentives last year were Visa gift cards. In the past they have offered a free 3-day cruise, $500 off airfare (that only to places like China and Australia for certain dates), and long ago there was a free child with paying adult and probably some others I've forgotten. But they might not offer anything. Generally they start out with the lowest price when they release the itineraries and raise the prices as the trips fill up.