What is the main lesson that is demonstrated by the St. Petersburg Paradox?

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….Finite St. Petersburg lotteries.

How do you solve the St. Petersburg Paradox?

The paradox known as the St. Petersburg Paradox is obtained by a simple coin flip game. The rules are simple: keep flipping until you get tails. If your first flip is a tails, then you win $2; if your first tails is on the second flip, then you win $4; if your first tails is on the third flip, you win $8, etc.

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.

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).

What is Bernoulli hypothesis?

Bernoulli’s hypothesis states a person accepts risk both on the basis of possible losses or gains and the utility gained from the action itself. The hypothesis was proposed by mathematician Daniel Bernoulli in an attempt to solve what was known as the St. Petersburg Paradox.

What is expected utility function?

“Expected utility” is an economic term summarizing the utility that an entity or aggregate economy is expected to reach under any number of circumstances. The expected utility is calculated by taking the weighted average of all possible outcomes under certain circumstances.

Is the Banach Tarski paradox real?

The strong form of the Banach–Tarski paradox is false in dimensions one and two, but Banach and Tarski showed that an analogous statement remains true if countably many subsets are allowed. Tarski proved that amenable groups are precisely those for which no paradoxical decompositions exist.

What was Bernoulli’s error?

The error that Bernoulli made, a psychological error–a big one, actually–was he decided to look at the outcome of the gamble and the utility of that outcome. He describes it as the utility of the state of wealth that would ensue, depending on what happened.

How do you play the St Petersburg paradox?

The standard version of the St. Petersburg paradox is derived from the St. Petersburg game, which is played as follows: A fair coin is flipped until it comes up heads the first time. At that point the player wins \\ (\\$2^n,\\) where n is the number of times the coin was flipped. How much should one be willing to pay for playing this game?

What is the origin of the St Petersburg paradox?

The standard version of the St. Petersburg paradox is derived from the St. Petersburg game, which is played as follows: A fair coin is flipped until it comes up heads the first time. At that point the player wins $2n, where n is the number of times the coin was flipped.

Can ergodic theory solve the St Petersburg paradox?

Ole Peters thinks that the St. Petersburg paradox can be solved by using concepts and ideas from ergodic theory (Peters 2011a). In statistical mechanics it is a central problem to understand whether time averages resulting from a long observation of a single system are equivalent to expectation values.

Does cumulative prospect theory restore the St Petersburg paradox?

Cumulative prospect theory is one popular generalization of expected utility theory that can predict many behavioral regularities ( Tversky & Kahneman 1992 ). However, the overweighting of small probability events introduced in cumulative prospect theory may restore the St. Petersburg paradox.