What is described in the St Petersburg Paradox?
The St. Petersburg paradox is a situation where a naive decision criterion which takes only the expected value into account predicts a course of action that presumably no actual person would be willing to take.
What is certainty equivalence?
The certainty equivalent is a guaranteed return that someone would accept now, rather than taking a chance on a higher, but uncertain, return in the future.
What is the problem of St Petersburg Paradox?
The St. Petersburg Paradox is based on a simple coin flip game with an infinite expected winnings. The paradox arises by the fact that no rational human would risk a large finite amount to play the game, even though the expected value implies that a rational person should risk any finite amount to play it.
What was Daniel Bernoulli’s solution to the St Petersburg Paradox?
Accepting this leads to a paradox; no reasonable person is prepared to pay the predicted large sum to play the game but will only pay, comparatively speaking, a very moderate amount. This paradox was ‘solved’ using cardinal utility.
What is the theoretical expectation value of the St Petersburg game?
The St. Petersburg Paradox. The ‘expected value’ of the game is the sum of the expected payoffs of all the consequences. Since the expected payoff of each possible consequence is $1, and there are an infinite number of them, this sum is an infinite number of dollars.
How much would you pay to play the St Petersburg Paradox?
People routinely play such lotteries for five dollars or less. So the price to play the St. Petersburg game should probably not exceed a few dollars.
What is the certainty equivalent formula?
Furthermore, your certainty equivalent CE of the gamble that will pay the random monetary amount X should be the amount of money that gives you the same utility as the expected utility of the gamble. Thus, we have the basic equation U(CE) = E(U(X)).
What is the certainty equivalence of a lottery?
The certainty equivalent of a lottery is the amount of money you would have to be given with certainty to be just as well-off with that lottery.
How much does the St Petersburg Paradox cost?
Petersburg game, and suppose that you’re willing to pay an entrance fee of only $20 to play. The reason you’re not willing to go higher is your risk-aversion.
Who developed a theory of diminishing marginal returns to explain the St Petersburg Paradox?
1.1 Diminishing marginal utility. Daniel Bernoulli was the first to argue, in his explanations of the St. Petersburg paradox, that the marginal value of money to an individual diminishes as his wealth rises (Bernoulli, 1738).
How did the St Petersburg paradox get its name?
However, from the description above, you probably wouldn’t be willing to pay much. After all, there is a 50% probability of winning nothing. This is what is known as the St. Petersburg Paradox, named due to the 1738 publication of Daniel Bernoulli Commentaries of the Imperial Academy of Science of Saint Petersburg .
How much do you win in the St Petersburg paradox?
In the St. Petersburg game the monetary values of the outcomes and their probabilities are easy to determine. If the coin lands heads on the first flip you win $2, if it lands heads on the second flip you win $4, and if this happens on the third flip you win $8, and so on.
How is the value of an uncertain prospect obtained?
According to this principle, the value of an uncertain prospect is the sum total obtained by multiplying the value of each possible outcome with its probability and then adding up all the terms (see the entry on normative theories of rational choice: expected utility ).