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QBUS6320 Tutorial 2

Problem 1: (The Wine Dealer)

A wine dealer has a customer who is willing to pay ✩15,000 for two identical vintage bottles of wine.  The importer of the wine is currently holding 3 bottles in stock and has offered to sell the dealer two bottles for ✩5,000 each.  If the dealer decides to wait for a week, there is a probability of 0.3 that the importer will have sold no bottles, and a probability of 0.4 that one bottle will be sold during the week.  The price of a bottle will be ✩4,000 next week. If the dealer decides to wait an additional week, the price of a bottle from the importer will go down to ✩3,000. Assuming that the importer has three bottles in stock at the beginning of the second week, the probabilities for sales in week 2 are identical to those in the first week. If, on the other hand, he only holds two bottles at the beginning of the week 2, there is a 0.6 probability that he won’t sell any bottles during the week. Any bottle left at the end of week 2 will be donated to charity by the importer. In any case, the customer is only interested in purchasing two identical bottles. What is the best policy in terms of EMV?

Problem 2: (The Chess Game)

Bobby Fisher has accepted the challenge to compete against the powerful chess computer “deep blue”. They will play a series of 2 games, where a victory awards 1 point, a draw awards 0.5 points and a loss awards no points.  In each game Fisher can choose one of two strategies: offensive or defensive.

If he chooses an offensive strategy, his chances of winning are 0.45, and his chances of losing are 0.55 (no possibility of a draw).

If he chooses a defensive strategy, he may win (0.2), finish in a draw (0.3) or lose (0.5). An overall victory is obtained by accumulating at least 1.5 points.

What is the best strategy (that  will  maximize  the probability  of an  overall  win  not  his expected score) for Fisher?