Sleeping Beauty problem
The Sleeping Beauty problem in decision theory illustrates a (possibly temporal) time inconsistency between belief and optimal behavior in classical decision theories:
- Suppose Sleeping Beauty volunteers to undergo the following experiment, which is described to her before it begins. On Sunday she is given a drug that sends her to sleep, and a coin is tossed. If the coin lands heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday, given a second dose of the sleeping drug that makes her forget the events of Monday only, and awakened and interviewed again on Tuesday. The experiment then ends on Tuesday, without flipping the coin again.
- Beauty wakes up in the experiment and is asked, "With what subjective probability do you believe that the coin landed tails?"