Abstract
It has been accepted for over 270 years that the expected monetary value (EMV) of the St Petersburg game is infinite. Accepting this leads to a paradox; no reasonable person is prepared to pay the predicted large sum to play the game but will only pay, comparatively speaking, a very moderate amount. This paradox was ‘solved’ using cardinal utility. This article demonstrates that the EMV of the St Petersburg game is a function of the number of games played and is infinite only when an infinite number of games is played. Generally, the EMV is a very moderate amount, even when a large number of games is played. It is of the same order as people are prepared to offer to play the game. There is thus no paradox. Cardinal utility is not required to explain the behaviour of the reasonable person offering to play the game.
Highlights
It has been accepted for over 270 years that the expected monetary value (EMV) of the St Petersburg game is infinite
The purpose of this article is to demonstrate that contrary to the accepted view, the St Petersburg game does not lead to a paradox at all
In all cases the amount the EMV, once correctly determined, predicts that his wager is moderate and this is in accordance with common experience
Summary
The position of a single game[19] is considered. It seems to me the source of the paradox stems from the irrational assumption that the EMV can be applied when a large number of games are played or when a single game is played. To accept the traditional view that the EMV of a single game is infinite or a large number is to ignore the possibility of any of the lower, high probability outcomes When a single game is played, the EMV is of little use and an alternative approach is needed It must be decided how much should Paul be prepared to pay to play this single game with this range of outcomes and probabilities? The EMV may not, where a single game is played be of much assistance to Paul, Arrow (1974,415) correctly points out that probabilities are relevant, even when a single game is played He wrote, ‘[w]hile it may seem hard to give justification for using probability statements when the event occurs only once ... This range is in line with the collective wisdom of history[21]
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