# Auction

An auction is a process by which a person or persons sell an item to buyers by the process of bidding. There are several different ways that items can be auctioned off.

## Types of Auctions

### English Auction

An English auction is one of the most common auctions, the one where people think about an auctioneer and his rapid delivery. It is also popularized by the auction website eBay.

## Strategies

For a bidder, the strategy is to always bid less than what you believe the item to be, assuming that your valuation is higher than the other bidders. A bidder's value of an item may be lower or higher than the actual retail value of the item for auction, and it differs amongst potential bidders (for example, hard-to-find popular retail items are usually sold for higher than the actual retail price on eBay).

In the case of a second-price auction, it is advantageous to bid your true value, assuming that it is higher than all the other bidders valuations.[2]

## Auctions & Game Theory

An example using game theory is listed below. In this case, if both players bid the same amount, then the payout in parentheses is assumed to be half of the value, as they are equally likely to win the auction (usually through some means of a tie-breaker). The values in parentheses are (Bidder #1 bid - Bidder #1 true value, Bidder #2 bid - Bidder #2 true value). If one player bids higher than the other, the other bidder gets 0 (they don't get the item and don't spend any money). The Nash equilibriums are marked with an asterisk:

Bidder #2 bids $3 (overbid) Bidder #2 bids$2 (their true value) Bidder #2 bids $1 (underbid) Bidder #1 bids$3 (overbid) (-1, -0.5) (-2, 0) (-2, 0)
Bidder #1 bids $2 (overbid) (0, -1) (-.05, .05) (0, -1) Bidder #1 bids$1 (their true value) (0, -2) (0, 1)* (0, .05)*

In this case, Bidder #1 has a dominant strategy of bidding $1. Therefore, if Bidder #2 bids$2, they will win the auction. For this case, if you know what another person values an item at, shave your bid to their value, and do not go over yours.[2]

## References

1. Penny auctions promise savings, overlook downsides USA Today, 02/06/2011
2. Gardner, Roy. Games for Business and Economics; John Wiley & Sons, Inc.; Hoboken, New Jersey. (2003)