The five Dukes of Earl are scheduled to arrive at the royal palace on each of th
ID: 1177930 • Letter: T
Question
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 kings place, becomes the new king, and awaits the next Dukes arrival. If he supports the king, all subsequent Dukes cancel their visits. A Dukes first priority is to remain alice, and his second priority is to become king.
a. Express the game as an extensive form game.
b. Who is king on May 6?
Explanation / Answer
The first duke.
If duke 5 ever gets to visit, he%u2019ll definitely kill, since he%u2019ll be safe afterward.
If duke 4 ever gets to visit, he%u2019ll definitely support, since when 5 goes, he%u2019ll kill.
If duke 3 ever gets to visit, he%u2019ll definitely kill, since when 4 goes, he%u2019ll support.
If duke 2 ever gets to visit, he%u2019ll definitely support, since when 3 goes, he%u2019ll kill.
If duke 1 ever gets to visit, he%u2019ll definitely kill, since when 2 goes, he%u2019ll support.
So 1 visits, kills the king, 2 supports, and all further visits are canceled.