You are a contestant on Who Wants to be a Millionaire. You have already answered the $250,000 question, and now must decide if you would like to answer the $500,000 question. You can choose to walk away at this point with $250,000 in winnings, or you may decide to answer the $500,000 question. If you answer the $500,000 question correctly, you can then choose to walk away with $500,000 in winnings or go on and try to answer the $1,000,000 question. If you answer the $1,000,000 question correctly the game is over, and you win $1,000,000. If you answer either the $500,000 or the $1,000,000 question incorrectly, the game is over immediately, and you take home “only” $32,000.

A feature of the game Who Wants to be a Millionaire is that you have three lifelines―namely 50-50, ask the audience, and phone a friend. At this point (after answering the $250,000 question), you have already used two of them, but you have the phone a friend lifeline remaining. With this option, you may phone a friend to get their advice on the correct answer to a question before answering it. You may use this option only once (i.e., you can use it on either the $500,000 question or the $1,000,000 question, but not both). Since your friends are all smarter than you are, phone a friend improves your odds for answering a question correctly. Without phone a friend, if you choose to answer the $500,000 question you have a 65% chance of answering correctly, and if you choose to answer the $1,000,000 question you have a 45% chance of answering correctly (the questions get progressively harder). With phone a friend, you have an 70% chance of answering the $500,000 question correctly, and a 55% chance of answering the $1,000,000 question correctly.

1. Use TreePlan to construct and solve a decision tree to decide what to do. State (in words below the tree) what is the best course of action, assuming your goal is to maximize your expected winnings.

2. Copy the worksheet from part a (hold down control (PC) or option (Mac) and drag the tab for 1a to create a copy of that tab, and then relabel the new tab 1b. Using the exponential utility function to account for your level of risk aversion, re-solve the decision tree. Include on the spreadsheet a brief description of how you determined the RT value that was appropriate for you to use for the exponential utility function (i.e., describe the process and specific gamble that you considered)*. Does the best course of action change?

* There is a “bug” associated with the exponential utility function and RT value with TreePlan:

Having an RT value that is way lower than the payoffs in the tree (over 1000 times lower) can lead to numerical issues (with #NUM displayed for some of the results). Some of the payoffs in the question at hand are up to $1 million. If you use an RT value of less than $1 thousand or so, the payoffs are all so much larger than the RT value that it leads to the exponential function it uses to calculate utility to have issues calculating properly. So, even if your true RT value is less than $1 thousand, you will need to use a value of at least $1 thousand in order to get results from your model.

Answer rating: 100% (QA)

a Use Tree Plan to construct and solve a decision tree The steps are shown below Step 1 In the Addin menu click on TreePlan Decision Tree Then a dialogue box will open After that click on new tree The ... View the full answer