The Petersburg Paradox -- A Con Game?

by Lloyd S. Shapley


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A logical analysis of a 259-year-old paradox sometimes employed to attack the use of expected monetary values in decision theory or game theory. In the "Petersburg game," first propounded by Nicolas Bernoulli in 1713, a person who is indifferent to risk is asked to pay a large entrance fee to a gambling game in which he will receive an uncertain payoff of infinite expected value. From the nature of the game, however, it is apparent that no rational person would accept this offer. This paper specifies a sufficient reason: that no rational person would believe the payoff. Hence, the Petersburg game does not expose any logical or mathematical absurdity in a risk-neutral utility for money. Moreover, the empirically absurd conclusion that it leads to rests on an additional, easily overlooked assumption about the credulity of the gambler — an assumption that is itself empirically absurd.

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