Question

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?

Answer 1

Answer (a) :

  From the above decision tree, we can see that We have the Option to Accept or Reject the Offer, if we Do not accept the offer then there is no further offer of drug in future and we live a healthy life. If we decide to accept the offer, then we have the pleasure to enjoy the offer for once, then after that we again have the option to accept or reject the offer for the second time, here if we choose to reject the offer, then there is no more drug in future and our is still secure. However, if we choose to accept the offer for the Second time, then hence forth it starts to impact our brain and we will now be impacted with life threatening brain disease. Our future is now not secure.

Answer (b) : Given the preferences, we should always decide not to try the drug for the first time itself. It is always better to keep off diseases and physical illness as far as possible in order to live a healthy life. It is very tempting to attempt to accept the drug offer for the first and only time and eject it in future since it is free, but it is still advisable not to try the drug at all, since once we have taken the drug , it will start the addiction and we will be tempted to try the drug again and again.

Answer (c) : In light of the given information that 40% of the people who tried the drug for the first time became addicted to it and were unable to stop the drug consumption after the first attempt , while the remaining 60% people did not become addicted and were able to use it once, we should still keep away from trying the drug, even for the first time , when it is free and less people get addicted comparatively. We cannot be 100% sure as to whether we will get addicted or not after the first consumption of the drug. It is always advisable not to take any risk on life threatening drugs. Hence, we should refrain from the consumption of the drug.

Answer (d) : If we represent the decision to try the drug and reject as lotteries, then there is 60% more probability that the lottery will be that we are getting addicted to the drug after the first consumption itself and we start consuming the drug again and again in future. This repeated consumption of the drug will prove detrimental to our health.

Answer (e) : The necessary and more than enough condition for us to reject the initial offer to try the drug is the life-threatening nature of the drug. Since the drug will prove detrimental to our health, this condition is the necessary and more than enough reason to not try this drug at all and refrain from it.