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Pirates and Laptops
Posted 14 January 2012 - 03:34 AM
100 pirates need to allocate 100 identical laptops among them. Their democratic system works as follows:
All pirates are ranked by their seniority (all pirates have different ranks). First, the most senior pirate proposes a plan that states exactly how many laptops each pirate gets. The 100 pirates vote on the plan and it passes at least half of the pirates vote for it. If it passes, all pirates take their laptops and go home. If it fails, the one who proposed the plan (the most senior pirate in this case) is killed, and the second most senior pirate takes his place and proposes his plan.The same process is repeated in the order of seniority until someone's plan is passed.
Assume every pirate makes his decision based on the following priorities:
1. He doesn't want to die.
2. Given he's not going to die, he would prefer to get as many laptops as possible.
3. Given he's going to get the same number of laptops, he would prefer as many other pirates to die as possible.
Also assume every pirate is logical, rational, and selfish (wants as many laptops as possible and doesn't care what anyone else gets as long as it doesn't affect him) and knows everyone else is the same. What will happen? i.e. whose proposal will be passed and what is the proposal?
Posted 14 January 2012 - 07:00 AM
I feel like not posting the solution, if only because I'm curious to see what people invent. Here's a hint, though...Spoiler for My solution
Posted 14 January 2012 - 10:53 AM
Posted 14 January 2012 - 12:31 PM
pirates, first pirate proposes 99:0:1 third one will accept it (if no this proposal couldn't be approved and first will be killed and second one proposes 100:0 and he gets all laptop leaving third with nothing). If there were 4 pirates first pirate proposes 99:0:1:0 and third support him (or first one dies and he gets nothing). If there were 5 pirates first one proposes 98:0:1:0:1 and gets third and fifth's support. And so on; if 100 pirates were present, first pirates propose 51:0:1:0......................:1:0:1:0 and this will won half the vote. (this is my first attempt and may have errors )
Posted 14 January 2012 - 04:46 PM
Posted 14 January 2012 - 05:00 PM
I don't think there is a hard set rule on this but most posters do monitor, sometimes giving additional clues, answering questions and giving credit to progress toward the answer as well as congtaatulations to the solver.
Question: This is only my second topic posted, am I supposed to say when someone gets the answer?
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