Suppose that you and two other people are competing in a third-price, sealed-bid auction.
In this auction, players simultaneously and independently submit bids. The highest bidder wins the object but only has to pay the bid of the third-highest bidder. Sure, this is a silly type of auction, but it makes for a nice exercise.
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 action, yet 20 is not a best-response action.