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Consider the following simple die game. You roll 1 die, once. The payoff depends on the roll of the die. Positive numbers reflect amount you earn, while negative numbers represent a payment you must make. Earn: If the outcome is 1 or 2: +\$15 Pay: If the outcome is 3: -\$12 Pay: If the outcome is 4: -\$30 Earn: If the outcome is 5 or 6: +\$36

For numeric answers include only the number, without the sign.

• Are you willing to play this game (Yes or No)?

Yes

• What is your expected payoff from this game. This is the amount you are willing to pay up-front to play the game. (You may need to round your answer to a whole number)? This is the amount you should be willing to pay the play the game. Consider the following variation of this game. First you roll the die. After you see the outcome of the die, you decide whether you want to play the game. This is called “payoff under Perfect Information.” • What is your expected payoff under perfect information, before rolling the die (you may need to round your answer to a whole number)? • By how much does your payoff increase when you see the result before deciding (you may need to round your answer to a whole number)?

This is the “Value of Perfect Information”. It represents the amount you would pay to know the result before making the decision.

In a more general case, if research or analytical forecasting were effective at predicting the future, this is how much that research would be worth.

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