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Question: 2 a friend if you can call him that has...

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2. A friend (if you can call him that!) has offered to let you try (for free) a new recreational drug, which is supposed to induce strong sensations of pleasure. You can reject or accept. If you reject, he will give up on you and never offer it again. If you accept (that is, you try the drug) then you know that he will come back later and offer it to you again (this time at a price). At that later time you will, again, have a choice between accepting and rejecting. You have done some research on this drug and found out that a one-time use will not cause any damage to your body, but repeated use (even only two times) will cause damage to the brain. Your most preferred outcome is a one-time-only use, while the worst outcome is repeated use (a) Represent your decision problem as a decision tree (b) What will you decide, given your preferences? Assume now that the research you did also reveals that 40% of the people who tried the drug in the past became addicted to it and were unable to stop after the first attempt, while the remaining 60% did not become addicted and were able to use it only once (if they so chose) (c) Represent your decision problem in light of this information. (d) Represent the decision to try the drug and the decision to reject the initial offer as lotteries. (e) If you satisfy the axioms of expected utility, what is a necessary and sufficient condition for you to reject the initial offer to try the drug?

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