St Petersburg Paradox Explained

Consider figure 17 1 in which on the x axis the quantity of money thousands of rupees and on the y axis marginal utility of money rupees to an individual are measured. If it falls heads then the player is paid one rouble and the game ends.

St Petersburg Paradox Wikipedia

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St petersburg paradox explained. Let s begin by calculating probabilities associated with this game. Petersburg lottery is a paradox related to probability and decision theory in economics it is based on a particular theoretical lottery game that leads to a random variable with infinite expected value i e infinite expected payoff but nevertheless seems to be worth only a very small amount to the participants. Nicolas bernoulli suggested the st petersburg game nearly 300 years ago which is widely bel ieved to produce a paradox in decision theory.

The standard version of the st. Petersburg paradox was introduced by nicolaus bernoulli in 1713. Saint petersburg paradox the saint petersburg paradox is a theoretical game used in economics to represent a classical example were by taking into account only the expected value as the only decision criterion the decision maker will be misguided into an irrational decision.

Petersburg paradox named due to the 1738 publication of daniel bernoulli commentaries of the imperial academy of science of saint petersburg. The probability that a fair coin lands heads up is 1 2. Petersburg paradox is the name now given to the problem rst proposed by daniel bernoulli in 1738.

Petersburg paradox is a situation. Petersburg paradox or st. Petersburg game which is played as follows.

The payouts double for each toss that lands heads and an in nite expected value is obtained. If it falls tails then it is tossed again and this time if it falls heads the player is paid two roubles and the game ends. A graphic illustration will make clear bernoulli s solution to the paradox.

A fair coin is flipped until it comes up heads the first time. Art of problem solving s richard rusczyk discusses an expected value paradox involving coin flipping. This is what is known as the st.

This belief stems from a long standing mathematical. Bernoulli proposes a coin ip game where one ips until the coin lands tails. It is in this way that bernoulli resolved st.

A coin is tossed. Petersburg paradox is derived from the st. A paradox of decision making first presented to the st petersburg academy in 1738 by the swiss mathematician and physicist daniel bernoulli 1700 82.

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