Steven Landsburg set 10 questions for honors graduates at Oberlin College. #8 is a great undergraduate game theory exercise:
Question 8. The five Dukes of Earl are scheduled to arrive at the royal palace on each of the first five days of May. Duke One is scheduled to arrive on the first day of May, Duke Two on the second, etc. Each Duke, upon arrival, can either kill the king or support the king. If he kills the king, he takes the king’s place, becomes the new king, and awaits the next Duke’s arrival. If he supports the king, all subsequent Dukes cancel their visits. A Duke’s first priority is to remain alive, and his second priority is to become king. Who is king on May 6?
visor volley: BoingBoing.
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December 8, 2009 at 2:05 pm
A
The fifth duke will definitely kill whoever is the king, so the 4th will definitely support, which means the 3rd will definitely kill, which means the 2nd will definitely support, which means the first one will definitely kill. So the first one will be the King, the second will support and no one else will show up.
December 8, 2009 at 2:34 pm
mike
in which case the first duke was not very smart. wouldn’t he support, meaning the king will remain the king?
December 8, 2009 at 3:58 pm
A
Mike,
If the first duke supports the king, then the first duke survives and no one else shows up.
If the first duke kills the king then the second duke support him and no one else shows up. In this case the first duke survives and becomes the king.
For Duke #1 killing is clearly a better option than supporting.
Best,
December 8, 2009 at 4:58 pm
Jason
I disagree.
The first Duke will kill the king for the reasons you stated (he’s obviously a smart guy since he got there first). The second Duke will kill the first Duke because the second Duke does not have anywhere close to an undergraduate understanding of game theory, has never heard of backwards induction, and is blinded by his ambition. He figures this is his one chance to be King, and that he’ll convince the third Duke to support him since otherwise the fourth Duke will just kill the third. He figures wrongly however, since the third Duke kills the second Duke realizing that the fourth Duke *will* in fact support him rather than be killed by the fifth Duke. This is what transpires, so the third Duke ends up being king.
December 8, 2009 at 5:41 pm
Azriel
I might not be the brightest bulb in the bunch…but considering the facts…..either the 5th duke would be king (meaning all dukes killed the king), or the original king would remain king, since a dukes 1st objective is to stay alive, the 1st visiting duke would support the king and all is done….
waiting in the wings to become king while others do the dirty work…[evil]hahahahahahahahahahahahah[/evil]
December 8, 2009 at 5:53 pm
piffle_dragon
backwards induction.
“A” is correct.
December 8, 2009 at 10:23 pm
knickerbocker
piffle dragon is right! Takes a Berkeley economist to know one. How is school by the way?
December 9, 2009 at 12:12 am
piffle_dragon
haha! Despite the budget, they still manage to teach us game theory.
I forget, where are you? Stanford, right? You like the defeat we dealt you guys in both big games?
If Stanford is incorrect, ignore that part…
December 8, 2009 at 6:33 pm
Dan
‘A’, indeed, is correct. However, if there were an odd number of dukes visiting, the king would still live, supported by the first duke. So bad move on his part inviting 5.
December 9, 2009 at 12:47 am
Jason
I don’t see why everyone thinks common knowledge of perfect rationality among medieval Dukes is a reasonable assumption…
December 9, 2009 at 4:13 pm
piffle_dragon
I thought we were doing economics. Who said anything about reasonable assumptions?
December 9, 2009 at 1:24 am
James Moore
I’m voting with Jason on this one. You think some Duke is definitely going to give up a chance to be king? Not happening. “Oh, there’s no way the next duke will kill me. I’m INVINCIBLE!”
As stated, involving dukes, the first duke has to support and the king stays the same. Or you have to restate this as a different kind of problem not involving greedy humans.
December 9, 2009 at 12:27 pm
Lyle_s
Only the first duke has to understand backwards induction so he can explain it to the second duke in a play for his support. If the second duke still doesn’t get it, well, what can you do?
I don’t know squat about game theory but it seems reasonable to me to that an undergraduate exercise would assume perfect rationality for the purpose of teaching.
December 12, 2009 at 5:14 pm
Anonymous
I agree with Jason.
Payoffs for for first three dukes are similar if they support the earlier king or kill the king. In later case they achieves all his objectives. But as this is not an infinite, problem, fourth duke has no option but to support as 5th duke has all the reasons to kills if he ever gets to make a visit. It becomes induction only after the 3rd duke decides to kill. Before that, risk and reward are pretty similar for supporting and killing the king.
I read someone saying the Duke 1 can reason with the Duke 2, well this is game theory, if your reasoning is true, I am sure Original King is not a dumb a** not to do the same thing.
August 28, 2021 at 5:51 am
Raphael Boleslavsky
…what if the number of possible Dukes who can visit is infinite?