Hi,
This is not related to java, it’s a maths problem.
I was wondering if any of the many smart maths people here could take a look at this problem about the St Petersburg paradox? I posted it on MathExchange but the dweebs there put my question ‘on hold’ for some reason.
I’ve tried to verify the below quoted statements on wikipedia because I think they’re mixed up: https://en.wikipedia.org/wiki/St._Petersburg_paradox#Expected_utility_theory
“For example, with log utility a millionaire should be willing to pay up to $10.94, a person with 1000 should pay up to 5.94, a person with 2 should pay up to 2, and a person with 0.60 should borrow 0.87 and pay up to 1.47.”
According to my simulation of results in a spreadsheet, I calculate that a natural logarithm utility function player with an initial wealth of 1000 (not a million) would pay a maximum of 10.95, rounded to the nearest cent, to participate once in the game. Here is a link to my spreadsheet simulation calculations that demonstrate my above findings that a player with 1000 initial wealth will only pay 10.95, not 5.94 as is stated in the wikipedia article. http://www.keithwoodward.com/random/wiki/StPetersburgParadoxBernoulliUtilitySolution.xlsx
Apologies if I’ve made a silly error. Just wanted to check.
Cheers,
Keith