Suppose that you and two other people are competing in a third-price, sealed-bid

Question

Suppose that you and two other people are competing in a third-price, sealed-bid auction. In this auction, player simultaneously and independently submit bids. The highest bidder wins the object but only has to pay the bid of the third-highest bidder. Suppose that your value of the object is 20. You do not know the values of the other two bidders. Demonstrate that, in contrast

with a second-price auction, it may be strictly optimal for you to bid 25 instead of 20. Show this by finding a belief about the other players’ bids under which 25 is a best response, yet 20 is not a best-response action.

Explanation / Answer

If the player would believe that the other players’ bid are 15 and 23. And If he bids 20, he will lose the game and will end up with 0 but if he bids 25, he will win the game and will get a payoff of 5. meaning 25 is a best-response action instead of bidding 20.

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