Alocal department store puts out products at an initial price, and every week the product goes unsold its price is discounted by 25% of the original price. if it is not sold after 4 weeks, it is sent back to the warehouse. there is a set of butcher knives that was just put out for the price of $200. your willingness to pay for the knives (your dollar value) is $180, so if you buy them at a price p, your payoff is u=180-p, and if you don't buy the knives, your payoff is 0. if you don't buy the knives, the chances that they are sold to someone else conditional on not selling in the week before are given as follows:
week 1: 0.2
week 2: 0.4
week 3: 0.6
week 4: 0.8
for example, if you do not buy during the first two weeks, the likelihood that it is available at the beginning of the third week is the likelihood that it does not sell in either weeks 1 or 2, which is 0.8 x 0.6 = 0.48.
at the beginning of which week, if any, should you run to buy the knives? (choose 0 if you should never buy the knives)