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# Vickerey

Suppose someone is selling some object in the following (kind of unusual) way. Everyone who wants to buy the object writes down a number. The person who wrote the highest number gets to buy the object, but gets charged the second highest number. All player's have a private value from the object, which is random.

Suppose that your value for the object is v.

1. Would you ever bid more than v regardless of how the other players bid? Explain.
2. Would you ever bid less than v regardless of how the other players bid? Explain.
3. What will happen in this auction?

#### Solution Preview

Suppose someone is selling some object in the following (kind of unusual) way. Everyone who wants to buy the object writes down a number. The person who wrote the highest number gets to buy the object, but gets charged the second highest number. All player's have a private value from the object, which is random.

Suppose that your value for the object is v.

1. Would you ever bid more than v regardless of how the other players bid? Explain.

This type of auction is called Vickerey (Second Price) Auction. The highest bidder wins the prize but pays the second highest bid. I would not bid for more than v irrespective of how the other player bid. Vickerey auctions have the property that bidding the item's true value is a player's optimal strategy.

If I bid more than my value for the object the utility of the bid would be less than the case where I bid my ...

#### Solution Summary

Vickerey is exhibited. The expert examines a big which is more than v regardless of how the other players bid.

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