You are indifferent between receiving 10,000 for sure or...

You are indifferent between receiving $$\$ 10,000$$ for sure or five times that amount if and only if a Pakistani wins a gold medal in the next Olympic Games. Your utility for money is linear. What is your subjective probability that a Pakistani will win a gold medal in the next Olympic Games?

Key Concepts

Indifference

Indifference in decision theory occurs when an individual feels equally satisfied with two alternative choices because they yield equal expected utilities. This state of indifference can be used to equate and solve for unknown probabilities or parameters in uncertain decision scenarios, highlighting the trade-off between guaranteed outcomes and risky prospects.

Subjective Probability

Subjective probability is the personal assessment of the likelihood of an event occurring, based on an individual’s own beliefs and information rather than on statistical frequencies. This concept is central to decisions under uncertainty where objective probabilities may not be available, and it reflects the decision maker's personal judgment about risks.

Risk Neutrality

Risk neutrality refers to the attitude in which an individual cares only about the expected value of outcomes, not the uncertainties around them. When a person is risk neutral, their utility function is linear, meaning the utility gained from a monetary outcome increases proportionally with the amount, regardless of variability in outcomes.

Expected Utility Theory

This theory posits that individuals make decisions by comparing the expected utilities of different outcomes, where each outcome's utility is weighted by the probability of that outcome. It offers a framework to evaluate uncertain choices by summing up the products of possible outcomes' utilities and their corresponding probabilities, ultimately guiding decision making under uncertainty.

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