Question: Consider the St. Petersburg paradox (Example), except that you receive $n rather than $2n if the game lasts for n rounds. What is the fair value of this game? What if the payooff is $n2?

Example: (St. Petersburg paradox). Suppose a wealthy stranger offers to play the following game with you. You will flip a fair coin until it lands Heads for the first time, and you will receive $2 if the game lasts for 1 round, $4 if the game lasts for 2 rounds, $8 if the game lasts for 3 rounds, and in general, $2n if the game lasts for n rounds. What is the fair value of this game (the expected payo↵)? How much would you be willing to pay to play this game once?