Adding a Utility Function to the St. Petersburg Paradox

Logic Level 3

The traditional resolution of the St. Petersburg paradox involves adding a utility function to the problem, taking into consideration diminishing marginal utility.

If the utility of winning nn dollars is a logarithmic function, specifically log(n)\log(n), then what is the expected payout, factoring in utility, that a player would get from playing the St. Petersburg paradox game? Put another way, if the value of nn diminishes log(n)\log(n), what is the break-even point such that a player should only pay less than this answer to play the game?

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