eXodia
2010-11-03, 16:59:58
Hallo!
Achtung: Viel Text. Wer keine Lust hat sich reinzudenken/lesen - bitte einfach überlesen =)
Was haltet ihr von meiner Lösung zu folgendem Problem:
Construct an order of the fruits (., ., ., .) such that if this order is used for the successive elimination procudure, cherry is chosen. A key lesson from this exercise is that, provided preferences are known, you may be able to "force" a certain choice outcome once you have the authority to set the agenda.
Die Preferences sehen wie folgt aus:
Iris Jay Kay
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banana durian apple
apple banana cherry
cherry cherry durain
durian apple banana
Bei Successive Elimination sehen die Game Trees immer "lustig" aus --> siehe Anhang.
Meine Lösung:
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Agenda: [C, D, B, A]
Begründung:
------------
Looking at the rules under the successive elimination game the preference order would be different. As it comes down to a choice between the first two fruits, and given that the only fruit cherry can beat is D, the agenda would be; [C, D, B, A]. The reason being that the other players would know that they cannot get their preferences passed. Using the looking forward, reasoning back approach we will see the following scenario play out;
Preferences
Iris: B > A > C > D
Jay: D > B > C > A
Kay: A > C > D > B
Given the agenda, we know that in the final round they would “vote” for “A”, Kay knows that “A” will never be passed given that Iris&Jay prefer “B” over “A”. This effectively reduces the preferences to;
Iris: B > C > D
Jay: D > B > C
Kay: C > D > B
However, looking at this Iris should know that “B” will never be passed given that Jay &Kay prefers “D” over “B”. This again reduces the preferences to;
Iris: C > D
Jay: D > C
Kay: C > D
So analysing this game, we see that in the first round the players have to decide on “C” versus “D”, because if they do not pass “C”, they know for a fact that “D” will be passed, given Jay&Kay’s preferences. Hence, in this game all players think strategically as they know that their preferences will not pass – leading Iris and Kay to vote for “C” in the first part of the game.
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Macht das eurer Meinung nach Sinn?
LG aus HK
Achtung: Viel Text. Wer keine Lust hat sich reinzudenken/lesen - bitte einfach überlesen =)
Was haltet ihr von meiner Lösung zu folgendem Problem:
Construct an order of the fruits (., ., ., .) such that if this order is used for the successive elimination procudure, cherry is chosen. A key lesson from this exercise is that, provided preferences are known, you may be able to "force" a certain choice outcome once you have the authority to set the agenda.
Die Preferences sehen wie folgt aus:
Iris Jay Kay
---------------------------
banana durian apple
apple banana cherry
cherry cherry durain
durian apple banana
Bei Successive Elimination sehen die Game Trees immer "lustig" aus --> siehe Anhang.
Meine Lösung:
--------------
Agenda: [C, D, B, A]
Begründung:
------------
Looking at the rules under the successive elimination game the preference order would be different. As it comes down to a choice between the first two fruits, and given that the only fruit cherry can beat is D, the agenda would be; [C, D, B, A]. The reason being that the other players would know that they cannot get their preferences passed. Using the looking forward, reasoning back approach we will see the following scenario play out;
Preferences
Iris: B > A > C > D
Jay: D > B > C > A
Kay: A > C > D > B
Given the agenda, we know that in the final round they would “vote” for “A”, Kay knows that “A” will never be passed given that Iris&Jay prefer “B” over “A”. This effectively reduces the preferences to;
Iris: B > C > D
Jay: D > B > C
Kay: C > D > B
However, looking at this Iris should know that “B” will never be passed given that Jay &Kay prefers “D” over “B”. This again reduces the preferences to;
Iris: C > D
Jay: D > C
Kay: C > D
So analysing this game, we see that in the first round the players have to decide on “C” versus “D”, because if they do not pass “C”, they know for a fact that “D” will be passed, given Jay&Kay’s preferences. Hence, in this game all players think strategically as they know that their preferences will not pass – leading Iris and Kay to vote for “C” in the first part of the game.
-----------------------------------------------------------
Macht das eurer Meinung nach Sinn?
LG aus HK