Suppose that you and two other people are competing in a thi

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.

Solution

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.