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# Third-Price Sealed Bid Auction

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Consider a third-price sealed bid auction: Suppose there are more than two bidders. Each potential bidder writes down a bid on a piece of paper. The buyer with the highest bid gets the item and has to pay the third highest bid. Is there a dominant strategy equilibrium for this auction? Make sure you exhaust all the possibilities!

https://brainmass.com/economics/preferences-choice/third-price-sealed-bid-auction-40615

#### Solution Preview

Let the representative bidder's expected value of the auction be V, and his bidding price to be B. The highest bid to be B1, the second highest B2, and the third B3. Assuming there's no cost of bidding, then the bidder has 3 choices:
B > V, B = V, and Bo < V

First, when B > V:
If B = B1, the bidder wins the auction, and has to pay B3, and his payoff is V - ...

#### Solution Summary

Is there a dominant strategy equilibrium for this auction? Make sure you exhaust all the possibilities!

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