So I'm taking this class this semester on the topic, (no worries, though, the FBI hasn't asked me to work for them yet). We analyze all sorts of games, and I'm just writing up the pirates game, modeling some business process (what did you expect? :)) :
Always something happening in these maths classes. :)
There are 5 pirates, ranked from the oldest (1) to the youngest (5). After having looted 100 pieces of gold, they return to their island and decide to share the loot and retire. The way they propose to do it is the following:
The youngest pirate proposes first an allocation for the gold (assume that each piece of gold is not divisible). Everybody votes either in favor or against the proposal. If the proposal has strictly more than 50% of 'Yes' votes, then it is implemented and the game ends. If not, then the pirate is killed and eliminated from the game. Then the youngest alive makes a proposal. We do this until one of the proposals is accepted.
For completeness, assume each pirate prefers to be alive rather than getting killed. Also assume that between killing and not killing, a pirate always prefer to kill another pirate.
9 Kommentare:
This is the story of the youngest pirate. He, like all the others, was perfectly egoist and rational...
So what did he do? He gave 2 gold pieces to the second-oldest pirate, one to the third-oldest, and kept the rest...
Then he bought a ticket to some lonely pristine paradise-like island and lived there unhappily ever after, utterly alone, because nobody wanted to be friends with him and he realised he couldn't have a serious conversation with the gold pieces ;-)
Cheers!
Jonas
PS: I like the story... and I guess he would have a majority, right?
Woah... yes!!
Congratulations on the subgame perfect Nash equilibrium! – I am thoroughly impressed. :)
Well, I have no idea what "subgame perfect" means... neither will I share how I came up with this result, at least not for the moment ;-)
Games like this are just fun because you can do serious business while playing; i like such problems a lot. On the other hand I often smile bitterly at the concept of "rationalism"... how can it be that the worst outcome is the most rational? So, for the unlikely case that you'll ever end up in prison with me, be assured of my loyalty :-)
If you like game-theorical puzzles/stories I recommend you this one:
http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/
(as well as this blog in general).
All the best
Clement
Ich bin da ganz anderer Meinung!
Seeräuber SR5 bietet SR2 3 Goldstücke und SR1 2 Goldstücke und überzeugt diese beiden, dass dies das beste Resultat ist, was sie erreichen können und überstimmt damit SR3 und SR4, denen er nichts anbietet. Damit bleiben ihm 95 Goldstücke.
Ich bin gespannt, wer dem widersprechen kann.
Nur, mit em Jonas sinere Variante chaner 97 Goldstueckli bhalte.
Ich finds aber vorallem iidruecklich, dass niemerd stirbt. :)
Yeah, I think this proposal would work as well.
But all things considered, this is still the story I like most:
The younges pirate proposed to split the loot equally amongst the five pirates. The others did not understand... why would anyone be altruistic? Especially the second youngest pirate was grumpy at first, but even he had to acknowledge that this was more money than he could ever expect to get.
Thus the proposal was accepted in unison, and the pirates lived happily ever after.
"Give, and it will be given to you. A good measure, pressed down, shaken together and running over, will be poured into your lap. For with the measure you use, it will be measured to you." -- Luke 6, 38
But I think this is easily said when talking about virtual gold pieces...
Ich gebe zu, meine Lösung war nicht optimal, aber die von Jonas funktioniert nicht!
SR2 kann damit rechnen, dass er ebenfalls 2 Goldstücke bekommt, sobald SR5 tot ist, weil dann SR4 an SR1 1 Goldstück und an SR2 2 Goldstücke abgibt und damit SR3 überstimmt, der in der dritten Runde sowieso 99 Goldstücke zu erhalten hofft. SR2 muss er aber um seine Stimme zu erhalten 2 Goldstücke geben, denn dieser kann damit rechnen, dass er in der dritten Runde auf sicher 1 Goldstück erhält und demnach gem. der letzten Regel lieber einen SR umbringt, wenn es keinen Vorteil gibt.
Somit wird SR2 nicht mit 2 Goldstücken in der ersten Runde zufrieden sein und zusammen mit SR1 gegen SR5 stimmen, was dessen Todesurteil bedeutet. Er wäre nur mit 3 Goldstücken zu gewinnen.
Also ist die egoistischste Lösung, dass SR5 2 Goldstücke an SR1 und 1 Goldstück an SR3 gibt. So bleiben ihm 97 Goldstücke, womit der Rest der Geschichte von Jonas stimmt.
Zudem bin ich auch der Meinung, dass die 2. Lösung von Jonas die Beste ist, also warum Mathematik studieren?
Zugegeben - es macht Spass!
e liebe Gruess
Papi
Beidi Möglichkeite funktioniered im Fall.. ich han jetzt dLösig formell ufgschriebe. :) Het nöd denkt, dass das so packend isch! :):)
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