This seems like such an obvious result, I imagine that there’s extensive discussion of it within the game theory literature somewhere. If anyone has a good paper that would be appreciated
This appears to be strongly related to the St. Petersburg Paradox—except that the prize is in utility instead of cash, and the player gets to control the coin (this second point significantly changes the situation).
To summarise the paradox—imagine a pot containing $2 and a perfectly fair coin. The coin is tossed repeatedly. Every time it lands tails, the pot is doubled; when it eventually lands heads, the player wins the entire pot. (With a fair coin, this leads to an infinite expected payoff—of course, giving the player control of the coin invalidates the expected-value calculation).
Pre-existing extensive discussion probably references (or even talks about) the St. Petersburg Paradox—that might be a good starting point to find it.
This appears to be strongly related to the St. Petersburg Paradox—except that the prize is in utility instead of cash, and the player gets to control the coin (this second point significantly changes the situation).
To summarise the paradox—imagine a pot containing $2 and a perfectly fair coin. The coin is tossed repeatedly. Every time it lands tails, the pot is doubled; when it eventually lands heads, the player wins the entire pot. (With a fair coin, this leads to an infinite expected payoff—of course, giving the player control of the coin invalidates the expected-value calculation).
Pre-existing extensive discussion probably references (or even talks about) the St. Petersburg Paradox—that might be a good starting point to find it.