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Question: How to design a desired mechanism g to implement a social choice function? Imagine that you want to sell an item. There are a bunch of prospective buyer agents. You want to sell it to the agent who wants it the most, but you can’t trust them to tell you the truth. The problem can be formally modeled as follows: a. θi in ℝ: types are the valuations. b. o in {1, ..., n}: index of agent who gets the item. c. ui(o, θi) = θi if o = i, and 0 otherwise. Question: How to design a desired mechanism g to implement a social choice function f(θ) = argmaxiθi�(�) = �� max� �� and with the mechanism g telling the truth is the dominant strategy for all the agents? (Hint: consider the Vickrey auction.)

          Question: How to design a desired mechanism g to implement a social choice function?

Imagine that you want to sell an item. There are a bunch of prospective buyer agents. You want to sell it to the agent who wants it the most, but you can’t trust them to tell you the truth. The problem can be formally modeled as follows:

a. θi in ℝ: types are the valuations.
b. o in {1, ..., n}: index of agent who gets the item.
c. ui(o, θi) = θi if o = i, and 0 otherwise.

Question: How to design a desired mechanism g to implement a social choice function f(θ) = argmaxiθi�(�) = ��� max� �� and with the mechanism g telling the truth is the dominant strategy for all the agents? (Hint: consider the Vickrey auction.)

Added by Kathryn R.

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