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Topic: Probability game (Read 1586 times) |
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Grimbal
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Probability game
« on: Sep 1st, 2009, 9:16am » |
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M people play a game to earn a prize.
Each person k selects secretly a number n[k].
After that, independently for each person, a random draw is made. It returns n[k] with probability 1/n[k] and 0 with probability 1-1/n[k].
The person with the highest result wins. If multiple people reach the maximum, they share the prize.
What is the best strategy? (i.e. how to maximize the earning expectancy).
(I don't know the answer myself. But it is related to a real-life problem)
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| « Last Edit: Sep 1st, 2009, 9:40am by Grimbal » |
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SMQ
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Re: Probability game
« Reply #1 on: Sep 1st, 2009, 9:37am » |
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If everyone draws 0, does everyone win (prize split M ways) or does no one win (prize unawarded)? The answer appears to make a lagre difference to the strategy with M small.
--SMQ
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--SMQ
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Grimbal
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Re: Probability game
« Reply #2 on: Sep 1st, 2009, 9:39am » |
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Good remark. It would be split among all.
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| « Last Edit: Sep 1st, 2009, 9:39am by Grimbal » |
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