Vickrey mechanism homework
Only two questions, but professional knowledge required, for more details please check files below. (Notice: use your own and unique example to answer question 2, otherwise it’s not acceptable.)
Exercise Set 3
Wednesday, February 27
1. Four pirates have left on an island their treasure chests, with values 100, 200, 300 and 400.
One day the pirates learned that the volcano on the island will erupt soon and destroy their treasures. Unfortunately their ship was wrecked and they could not reach the island. A fisherman comes along on a raft and offers help. He says to the pirates: “My raft is small and I can only bring back one treasure chest from the island before the volcano erupts. Write the
value of your treasure chest on the palm of your hand and show it to me so no one else can see. I will retrieve the chest of the one who shows me the highest value. When I come back, the owner of the chest I bring back will pay me, and the payment will be equal to the second highest value that was shown to me.” (i) What value should each pirate write down on his hand? Is it better for him to lie or to tell the truth? (ii) When each pirate acts optimally,
whose chest will be brought back by the fisherman? How much payment will he receive?
*** The question below is a bonus points assignment. If you choose to do it, the due date is
Monday, March 4. We will ONLY accept a TYPED answer.
2. Think of a real life situation where you can apply the Vickrey mechanism to induce people to
reveal truthfully their hidden information. Clearly describe the problem. Explain how you will
implement the Vickrey mechanism, and why people will “tell the truth.”
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