Question

The St. Petersburg paradox goes as follows. A fair coin is tossed repeatedly until it comes up heads. If the first heads appears on the nth toss, you win $2 n . First, show that the expected monetary value of this game is infinite (the paradox is that no one would actually pay a huge amount to play this game). Second, consider a possible resolution of the paradox: suppose your utility for money is given by a log 2 x b where x is the number of dollars you have. Suppose you start with 0 dollars, what is the expected utility of this game

Answer 1

a) attached below

b) 2a + b

Explanation:

a) show that the expected monetary value of this game is infinite

Given that the probability of getting first head on nth toss = $2^n

attached below is the prove

b) what is the expected utility of this game

using the Logarithm ;
`U(x) = a log_(2) n + b`

x = number of dollars you have

attached below is a detailed solution to the given problem