The municipality of Lisbon wants to sell a restored building and is planning an auction.

There are two buyers and each of them may value the building at 16 (million Euros) or at 9 (million Euros). Even though each buyer is aware of her type, the municipality only knows that each buyer may have a high valuation with probability 3/4 (and a low valuation with probability 1/4). The surplus for each type of buyer will be equal to the difference between her valuation and the price she ends up paying; and zero otherwise. Each type's reservation utility is 0. The municipality cares only about maximizing expected revenue.

Question

The municipality of Lisbon wants to sell a restored building and is planning an auction. 
 
 There are two buyers and each of them may value the building at 16 (million Euros) or at 9 (million Euros). Even though each buyer is aware of her type, the municipality only knows that each buyer may have a high valuation with probability 3/4 (and a low valuation with probability 1/4). The surplus for each type of buyer will be equal to the difference between her valuation and the price she ends up paying; and zero otherwise. Each type's reservation utility is 0. The municipality cares only about maximizing expected revenue.

Answer

In the optimal auction, if the municipality is faced with two low valuation agents, it will choose to sell the building to each of them with probability ½ each.

Answer

As long as buyers are risk neutral and their valuations are independent, an English auction or a Dutch auction would lead to the same expected revenue.

Answer

In the optimal auction, the expected revenue the municipality will receive from any agent is 7.5

Answer

In the optimal auction, a high valuation agent will receive a positive expected payoff.

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The municipality of Lisbon wants to sell a restored building and is planning an...

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