10 people are around the table on the 50'th floor. 100 dollars are in the middle of the table, and they need to split it between them. The first one presents an offer - how much will each one get. They all vote; if the offer is accepted (at least half the people support it) -they go by that offer. Otherwise, they throw the person who has made the offer out of the window, and the person on his right makes the next offer. What offer should first person make to maximize his share and stay alive?
2006-07-13 10:32:11 · 12 answers · asked by dan m 2 in Science & Mathematics ➔ Mathematics
Assume the only people left are #9 and #10-in this case #10 gets nothing and #9 votes for himself, thereby keeping all the money. So if #8 is perfectly rational, he will offer #10 $1 (which is the most he gets out of this arrangement) and keep $99 for himself, thereby ensuring 2 of 3 votes. #7, knowing this, could offer #9 $1 and be assured of his vote, and could also keep $99 for himself. Now, #6 must therefore bribe both #8 and #10, and once again $1 will be sufficient since under #7's plan they get nothing. Extrapolating from this pattern, we see that the optimal strategy for #1 is to give $1 each to #3, #5, #7, and #9 (which will be sufficient because under #2's strategy, they get nothing), and keep $96 for himself.
2006-07-13 10:51:30 · answer #1 · answered by Pascal 7 · 5⤊ 2⤋
Because only a majority of the people need to support a decision, the first person simply needs to ensure that half (or if an odd number, one less than half) agree to an equal sum plus his own, and that his own share is equal to or lesser than the others he wishes to agree. So divide the total amount by the number of people whom need appeasing (including the first person), and if uneven, then round up and give that amount to all the others, and the first person keeps the remainder.
With 10 people, he needs 5 people to agree plus himself. Thus, simply divide the $100 by 6, round it up, give this amount to 5 of the people, and keep the rest. This allows a $16.67 share for 5 people, a $16.65 share for him, and $0 for the remaining 4 people.
(This assumes, of course, that the agreed upon amounts are the final amounts received, and no arrangements are made beforehand for post-trading. Besides, post-trading would only work if the preparations could be discussed in secret. Otherwise, people around the table will know that they will be getting left out and vote accordingly, and the situation would revert back to the solution above.
If secret post-trading were in fact allowed, then the first person need only offer everybody else absolutely nothing and promise to trade them a larger share later, as large as $50/$50 in fact. Then, he pockets all $100 and simply does not give anybody else a single penny. If the others are intelligent enough to be wary about this deal *or* if he is obligated to keep any post-trade promises that he makes, then once again, the only reasonably acceptable offer would be the $16.67 mentioned above, any less and he would be voted out the window.)
2006-07-13 17:58:36 · answer #2 · answered by stellarfirefly 3 · 0⤊ 0⤋
If the first person offers $10 each, the others could throw him or her out of the window and split $11.11 each. The second person could offer that for everyone, but the others could throw him or her out to get $12.50 each. And so on.
The first person needs to make an offer that will be accepted by 5 of the 10, or only 4 other people.
10.00 + 11.11 + 12.50 + 14.29 + 16.67 = $64.57,
leaving $35.43 to split between five people to help sweeten the deal. This works out to $7.09, each.
I'd say the first person should offer
person 2: $18.19,
person 3: $19.59,
person 4: $21.38,
person 5: $23.76,
and keep $17.07 for himself or herself. Hopefully he or she would get the 5 needed votes to stay on the 50th floor.
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I really like Pascal's answer (the one after mine) better, though.
2006-07-13 17:49:55 · answer #3 · answered by Louise 5 · 0⤊ 0⤋
Each one should get 11 dollars, except the person making the offer. This latter would be getting one dollar and the assurance of everyone staying alive.
2006-07-13 17:42:20 · answer #4 · answered by droblivion 2 · 0⤊ 0⤋
he offers that each of the other 9 ppl get 10$ + and equal part of his share
2006-07-13 17:37:11 · answer #5 · answered by kevin h 3 · 0⤊ 0⤋
the offer i would make would be to begin on the first persons left side
2006-07-13 17:41:26 · answer #6 · answered by dwh 3 · 0⤊ 0⤋
He has to say that he gets $1 and everyone else gets $11.
Think about it -- even if they chuck him out the window and divide the money evenly, all but one of them would get $11.
2006-07-13 17:39:54 · answer #7 · answered by Anonymous · 0⤊ 0⤋
100/10=X
10 x 10=100
100/10=10
2006-07-14 15:18:12 · answer #8 · answered by Sk8erboi83 3 · 0⤊ 0⤋
10 dollars each, make everyone happy.
2006-07-13 17:35:34 · answer #9 · answered by corbeyelise 4 · 0⤊ 0⤋
5 bucks each person, in pocket, and order pizza.
2006-07-13 17:35:50 · answer #10 · answered by sawtooth_honey 4 · 0⤊ 0⤋