This is an important result, sometimes called the holy grail of competitive analysis.

One way to think about competitive analysis is bulk discounts. In life we’re constantly having to choose between quantity and discount. We could buy 1 item for a higher price, or say quantity 5 or 10 to get better discounts. The problem comes when we don’t know in advance exactly how many we’re going to need.

What should be our strategy for choosing how many to buy, and whatever the strategy is how well does it compare with having perfect knowledge upfront?