In an English auction, also known as an open ascending-bid auction, bidders start with a low price and gradually increase their bids until only one bidder remains.

In a first-price sealed-bid auction, the highest bidder wins and pays the amount of their bid, regardless of the bids submitted by other bidders.

In a second-price sealed-bid auction, also known as a Vickrey auction, bidders submit their bids simultaneously, and the highest bidder wins but pays the amount of the second-highest bid.

In a Dutch auction, also known as a descending-price auction, the price starts high and gradually decreases until a bidder is willing to accept the current price.

Overbidding is a bidding strategy where a bidder submits a bid that is significantly higher than the expected value of the item being auctioned, in an attempt to intimidate other bidders or secure the item at a higher price.

Underbidding is a bidding strategy where a bidder submits a bid that is lower than the expected value of the item being auctioned, in the hope of winning the auction at a lower price.

Bluffing is a bidding strategy where a bidder submits a bid that is intended to deceive other bidders about the true value of the item being auctioned, in an attempt to win the auction at a lower price.

Shill bidding is a bidding strategy where a fake bidder is used to artificially increase the price of an item being auctioned, in order to manipulate the outcome of the auction.

In a first-price sealed-bid auction, the Nash equilibrium is not for each bidder to submit a bid equal to their valuation of the item, as this would lead to the highest bidder paying more than their valuation.

In a second-price sealed-bid auction, the Nash equilibrium is for each bidder to submit a bid equal to their valuation of the item, as this will maximize their expected payoff.

Dutch auctions are commonly used for selling government bonds, as they allow the government to raise funds quickly and efficiently.

English auctions are commonly used for selling artwork, as they allow bidders to compete openly and drive up the price to reflect the true value of the artwork.

First-price sealed-bid auctions are commonly used for selling real estate, as they allow bidders to submit their bids privately and avoid being influenced by other bidders.

Second-price sealed-bid auctions are commonly used for selling commodities such as oil and gas, as they encourage bidders to submit their true valuations without fear of paying more than necessary.

In a first-price sealed-bid auction, a bidder's expected payoff is equal to the difference between their valuation of the item and the amount they bid, as they will win the auction if their bid is the highest and pay the amount of their bid.