Auctions are among the oldest methods of selling items, with recorded occurrences as early as 500 BC. While historically not as common as sale by fixed price or bargaining, the development and proliferation of the internet and information technology has made auctions into a common means of selling and buying items, both large and small. At its most basic, an auction is a set of rules by which an item is sold to one of several potential buyers. In this set of rules by which an item is sold to one of the several potential buyers. There are different types of auctions available.
- The First Price Auction: In a first price auction, each bidder simultaneously writes down his name and a number on a slip of paper and submits the paper to the auctioneer. The auctioneer turns over all the of the papers, the bidder who wrote down the highest number is given the item and pays the amount that is written on his slip. Under certain assumptions, this procedure is identical to the so-called Dutch auction, or descending price auction. The price begins at some incredibly high amount and drops at a predetermined rate, for example 10 cents per second. The auction ends when one of the bidders presses a button which keeps the price from falling further and pays an amount of money, equal to the posted price when he stopped the clock. The other bidders receive nothing and pay nothing.
- The second price auction: In second price auction, each bidder simultaneously writes down his name and a number on a slip of paper and submits the papers to an auctioneer. The auctioneer turns over all the papers and the bidder who wrote down the highest number is given the item and pays the second highest amount that was written by other bidders. Under certain conditions and assumptions the auction is similar to that of Button auction and auction of fish in Japan. The bidders will have their names on a board with lights next to their names. The auction begins with zero and ascends at a predetermined rate. As long as the lights next to the name of a bidder is still on, the participant is still in the auction. Each bidder can press a button which will turn off the lights. The last bidder to be in the auction with lights on will win the item and pays the price at which his previous bidder dropped out. This is similar to the selling procedure on eBay.
- The All-Pay Auction: In all-pay price auction, each bidder simultaneously writes downs his name and a number on a slip of paper and submits the papers to an auctioneer. The auctioneer turns over all of the papers, the bidder who wrote down the highest number is given the item but all bidders who wrote down the highest number is given the item but all bidders have to pay their bids.
- The Lottery: In a lottery, each bidder can write down only one of the two bids, “In” or “Out”. All those players that are “in” are required to pay a price p, and have an equal chance of winning the item. Those that are “out” pay nothing and do not have the potential to win anything. We can think of these situations as Bayesian Games. In these games, the set of players will consist of a number of bidders, usually two. Given their type, each player chooses a bid, that is what to write down on the slip of paper and submit to the auctioneer. Given this outcome, each player’s payoff is
Ui (Qi, Pi/ V1, V2) = ViQi – Pi
Thus, each player’s payoff is his or her value for the good multiplied by the quantity of the good that he or she receives, minus any payment she has to make. Crucially, each buyer’s payoff only on his or her own value, any other bidder’s value for the item is irrelevant to each bidder. If two buyers are interested in acquiring a new painting from a young artist. If one art dealer has a very high valuation, it may mean, for example, that he or she has a client lined up for this piece, and although the other dealer may not know the identity of the client for certain, the fact that the other dealer places a high value on the painting may be important to a given art dealer’s assessment of its value.
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