Lecture 23 revision summaries PDF

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Lecture 23 revision summaries...

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Lecture 22: Auctions

An eBay Auction • eBay and a number of other online auctions use “proxy bidding” rules. • Under a proxy bid, you enter a bid amount ($30), but what you pay is determined by the second highest bid ($20) plus a small increment ($0.1). • Suppose that you know your willingness to pay for an item for sale on eBay.

Common Auction Formats - Differences

• Open format: English Auction; Dutch Auction • Bidders at the same place (on the phone) • Bidders can observe others’ bids • Sealed-bid format: First-price auction; Second-price auction • Submit by mail/email • Bidders cannot observe others’ bids

Strategic Equivalence

• Why do we care? • We often observe English auction and Dutch auctions, but game theoretically, first-price and second-price auctions are easier to analyze. • Government Vehicle Auction: Which auction should the government use? Which auction generates higher revenue? • Need to understand how people compete (their strategies).

Second-price Auction • Suppose your valuation for the item is 𝑣𝑣. • Suppose 𝑟𝑟 is the largest bid from your rivals. (You do not

know what 𝑟𝑟 is.) • You win if your bid is higher than the largest bid 𝑟𝑟 from your rivals. • When deciding on your bid 𝑏𝑏, you should look for the best response to the (unknown) largest bid 𝑟𝑟 from your rivals. • Notice that 𝑟𝑟 can be larger or smaller or equal to your valuation, 𝑣𝑣.

Second-price Auction – What Went Wrong in NZ? • Problem: Low competition with a small number of bidders and weak bidders. • A student bid NZ$1 for a television license for a small city! • The government or the NERA (the consulting company used)

should have expected this problem to arise. • How to fix it: 1. Get more bidders through advertising (e.g., invite bidders from Australia) 2. Set a reserve price – substitutes for missing bidder competition. If you set a reserve price equal to the cost of the item, then you can ensure that you do not lose money.

An English (or ascending price) auction is strategically equivalent to a second price auction. • Implemented through proxy bidding: eBay. • Does not work well with little competition (New Zealand spectrum auction). • Reserve price helps. • Works very well if the number of bidders is large. • Advertisements help....