The St. Petersburg paradox is a famous thought experiment in probability theory and economics. It was introduced in the early 18th century by Daniel Bernoulli’s cousin, Nicolas Bernoulli. The paradox revolves around a hypothetical gambling game where a player pays an entry fee and flips a fair coin. If the coin comes up heads, the player wins double the entry fee, and the game continues until tails appears. The player’s payoff increases exponentially with each consecutive round of heads.
The paradox arises from the question of how much a rational player should be willing to pay to enter such a game. The expected value of the game is theoretically infinite, as the potential payoff grows indefinitely with each round of heads. However, most people are not willing to pay an astronomical amount to participate, leading to a tension between expected utility theory and actual human behavior.
Various solutions and extensions have been proposed to address the St. Petersburg paradox, such as considering diminishing marginal utility or introducing bounded rationality. The paradox remains a significant topic in decision theory and continues to spark discussions about risk aversion and rationality in economic decision-making.