Auction Mechanisms: Bidding Strategies and Outcomes

Fundamental Auction Concepts

Payoff: A bidder's payoff is their valuation for the item minus the price paid.

Social Surplus: This is the sum of the surpluses of all participants. The formula is: Seller's Surplus (p) + Winner's Surplus (v - p) + Loser's Surplus (0). Here, v is the winner's valuation and p is the price paid. Social surplus is maximized, and the auction is considered efficient, if the winner is the bidder with the highest valuation.

Types of Auctions

English Auction

This is a type of ascending auction where an auctioneer announces prices, and bidders accept or reject them.

• Winner: The last remaining bidder.
• Price: The second-highest price or bid.
• Information Revealed: The auctioneer learns the valuations of all bidders except for the winner.
• Dominant Strategy: Truthful bidding is the dominant strategy, making it strategy-proof.

Japanese Button Auction

A type of English auction where the price is displayed with an automatic increment. Bidders must hold down a button and are eliminated when they release it. This is an ascending auction.

• Winner: The last bidder still pressing the button.
• Price: The price displayed when the second-to-last bidder drops out.

English Outcry Auction

An ascending auction where bidders openly announce their prices.

• Winner: The highest bidder.
• Price: The highest price announced by the winner.
• Bidding Strategy: A bidder's strategy depends on how other participants bid.

Vickrey Auction (Second-Price Sealed-Bid)

Also known as a simultaneous second-price auction, buyers submit sealed bids.

• Winner: The participant with the highest bid.
• Price: The second-highest submitted bid.
• Dominant Strategy: Truthful bidding is the dominant strategy, making it strategy-proof.

First-Price Sealed-Bid Auction

This is a strategic normal form game where bidders submit sealed bids simultaneously.

• Winner: The highest bidder wins and pays the amount of their bid.
• Bidding Strategy: The strategy is complicated. Bidders may not want to bid their true valuation because their payoff would be zero. The goal is to maximize the probability that your bid is the highest while paying as little as possible.
• Optimal Strategy: Assuming n bidders and that your valuation, v_i, is the highest, the optimal strategy is to bid what you expect the second-highest valuation to be. This can be calculated as: v_i * [(n-1) / n].

Dutch Auction

A descending auction where the auctioneer starts with a high price that decreases until a bidder accepts it. This is an extensive form game and is strategically equivalent to a first-price sealed-bid auction. It is not strategy-proof.

• Advantages: This format is very fast and can make bidders nervous, potentially leading them to bid higher than they otherwise might.

First-Price vs. Second-Price Auction Comparison