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A mathematically correct solution is sampling by William Feller [8]. In this method, when the games of infinite number of times are possible, the expected value will be infinity, and in the case of finite, the expected value will be a much smaller value.

Samuelson resolves the paradox by arguing that, even if an entity had infinite resources, the game would never be offered. If the lottery represents an infinite expected gain to the player, then it also represents an infinite expected loss to the host.

No one could be observed paying to play the game because it would never be offered. As Paul Samuelson describes the argument:. Ole Peters thinks that the St.

Petersburg paradox can be solved by using concepts and ideas from ergodic theory Peters a. 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.

This is the case only for a very limited class of systems that are called " ergodic. Peters points out that computing the naive expected payout is mathematically equivalent to considering multiple outcomes of the same lottery in parallel universes.

This is irrelevant to the individual considering whether to buy a ticket since he exists in only one universe and is unable to exchange resources with the others.

It is therefore unclear why expected wealth should be a quantity whose maximization should lead to a sound decision theory. Petersburg paradox is only a paradox if one accepts the premise that rational actors seek to maximize their expected wealth.

The classical resolution is to apply a utility function to the wealth, which reflects the notion that the "usefulness" of an amount of money depends on how much of it one already has, and then to maximise the expectation of this.

In the standard St. Although this is an expectation value of a growth rate, and may therefore be thought of in one sense as an average over parallel universes, it is in fact equivalent to the time average growth rate that would be obtained if repeated lotteries were played over time Peters a.

Under this paradigm, an individual with wealth w should buy a ticket at a price c provided. This strategy counsels against paying any amount of money for a ticket that admits the possibility of bankruptcy, i.

If we assume the smallest payout is D 1 , then the individual will always be advised to decline the ticket at any price greater than.

Petersburg paradox and the theory of marginal utility have been highly disputed in the past. For a discussion from the point of view of a philosopher, see Martin Recently some authors suggested using heuristic parameters [9] e.

The expected output should therefore be assessed in the limited period where we can likely make our choices and, besides the non-ergodic features Peters a , considering some inappropriate consequences we could attribute to the expected value Feller From Wikipedia, the free encyclopedia.

This article includes a list of references , but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations.

October Learn how and when to remove this template message. Conceptual foundations of risk theory.

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