St. Petersburg Paradox

The St. Petersburg paradox is a theoretical problem in probability and decision theory that arises from a gambling game involving repeated coin flips. In this game, a player wins an amount that doubles with each tails outcome until a heads appears, leading to an infinite expected value of winnings. Despite this, players typically express reluctance to pay a high entry fee, indicating a discrepancy between expected value and actual willingness to pay. The paradox was first introduced by Nicolas Bernoulli in 1713 and later analyzed by his cousin Daniel Bernoulli, who suggested that the utility of money diminishes as wealth increases, leading to a more realistic assessment of the game's value. Various solutions have been proposed, including expected utility theory, which incorporates diminishing marginal utility, and probability weighting, which suggests that people undervalue unlikely outcomes. Additionally, the assumption of infinite resources for the casino has been challenged, with finite bankrolls leading to a more modest expected value. This paradox highlights the complexities of human decision-making in uncertain situations and has implications for economic theory and behavioral finance.

- The St. Petersburg paradox illustrates the conflict between infinite expected value and actual willingness to pay.

- Daniel Bernoulli's expected utility theory provides a resolution by considering diminishing marginal utility of money.

- Probability weighting suggests that people may neglect unlikely events, affecting their decision-making.

- The assumption of infinite resources for the casino is unrealistic; finite bankrolls lead to lower expected values.

- The paradox has significant implications for understanding human behavior in economics and finance.