St. Petersburg Paradox

Definition

The St. Petersburg Paradox is a famous problem in probability and economics that illustrates the conflict between expected value and actual decision-making under risk. In this paradox, a game offers a potentially infinite payout based on a coin toss, leading to an infinite expected value, yet most individuals are unwilling to pay a high entry fee to play the game, highlighting the limits of expected utility theory and the concept of risk aversion.

5 Must Know Facts For Your Next Test

1. The St. Petersburg game involves flipping a coin until it lands on heads, with the payout doubling for each tail flipped before the first head appears.
2. Although the expected payout can theoretically reach infinity, most people would only be willing to pay a small amount to enter the game due to their risk aversion.
3. This paradox highlights a discrepancy between mathematical expectations and human behavior when faced with high-stakes situations.
4. The St. Petersburg Paradox challenges traditional views of rational decision-making by emphasizing how emotions and cognitive biases influence choices.
5. Solutions to the paradox often involve modifying the utility function to reflect diminishing marginal utility of wealth, illustrating why individuals might reject high-risk gambles.

Review Questions

• How does the St. Petersburg Paradox illustrate the differences between expected value and actual decision-making in risk scenarios?
  • The St. Petersburg Paradox demonstrates that while the expected value of the game is theoretically infinite, individuals often choose not to participate due to their risk preferences. This situation shows that people do not make decisions purely based on mathematical expectations; instead, they factor in their emotional responses and fear of loss. The disparity between what is mathematically expected and what people are willing to stake reveals insights into human behavior regarding risk.
• Discuss how the St. Petersburg Paradox can be reconciled with expected utility theory and its implications for understanding risk aversion.
  • To reconcile the St. Petersburg Paradox with expected utility theory, one must consider that individuals derive utility from wealth in a non-linear fashion. By incorporating diminishing marginal utility into the analysis, where each additional dollar has less impact on overall satisfaction, it becomes clearer why people may only be willing to pay a small amount to enter the game. This perspective aligns with observed behavior and illustrates that people's risk aversion leads them to favor certainty over uncertain high payouts.
• Critically evaluate how the St. Petersburg Paradox has influenced modern economic thought regarding risk and decision-making under uncertainty.
  • The St. Petersburg Paradox has significantly impacted modern economic thought by challenging classical assumptions about rationality in decision-making under uncertainty. It has led to deeper investigations into how individuals assess risk and value potential outcomes, promoting concepts like prospect theory which accounts for behavioral biases in economic choices. The paradox encourages economists to consider psychological factors when analyzing decision-making processes, resulting in more nuanced models that better reflect real-world behaviors concerning risk and uncertainty.

Related terms

Expected Utility Theory: A theory that posits individuals make decisions based on the expected utility of different outcomes rather than the expected value, considering their risk preferences.

Risk Aversion: A behavioral characteristic where individuals prefer certain outcomes over uncertain ones, even if the uncertain option has a higher expected value.

Utility Function:

A mathematical representation of an individual's preferences, showing how much utility or satisfaction they derive from various levels of wealth or consumption.