CSV 886 Social Economic and Information Networks. Lecture 4: Auctions, Matching Markets. R Ravi

Transcription

1 CSV 886 Social Economic and Information Networks Lecture 4: Auctions, Matching Markets R Ravi ravi+iitd@andrew.cmu.edu

2 Schedule 2

3 Auctions 3

4 Simple Models of Trade Decentralized Buyers and sellers have to find each other (search costs) and agree on price (negotiation costs) Central exchange with competition Auctions set prices Centralized exchange Intermediaries setting fixed prices Faster search and clearing 4

5 Auction Theory Used in practice since ancient times Modeled as (Bayesian) Games Valuations of bidders: private or common Auction Types: Open Format or Sealed Bids Key issues of study Revenue Efficiency 5

6 Relationships Ascending Bid (English/Japanese) Auctions Descending Bid (Dutch) Auctions First Price Sealed Bid Auctions Second Price Sealed Bid Auctions 6

7 Online Auctions 7

8 Online Bids 8

9 What kind is an ebay auction? Ascending Bid (English) Auctions Descending Bid (Dutch) Auctions First Price Sealed Bid Auctions Second Price Sealed Bid Auctions 9

10 Final bid submission pattern 10

11 Second Price Auctions Model as a game Players are bidders Each has a private value for good auctioned off Strategy: Put in a bid Outcome: Highest bidder wins and pays second highest bid as price (ties?) Payoff? If not highest bidder, zero If highest bidder, private value minus second highest bid 11

12 Example Example: v(a) = $10, v(b) = $ 12 Bid(A) = $9, Bid(B) = $10 First price sealed bid auction outcomes: Winner: selling price = payoff (A)= payoff (B)= Second price sealed bid auction outcomes: Winner: selling price = payoff (A)= payoff (B)= 12

13 Second Price Auctions Bidding your true value is a dominant strategy [Vickrey 96 Nobel]. Why? Bid higher: Bid lower: 13

14 Second Price Auctions Bid only affects whether you win, NOT what you pay Truthful bidding also dominant strategy for ascending bid auction Second Price and Ascending Auctions are strategically equivalent with private valuations! 14

15 First Price Auction Bidding truthfully will leave no payoff for you Use probability distribution to model uncertain valuations: Bayesian game What would an optimal strategy look like? How will it change as number of bidders increase? 15

16 Two bidder second-price auction 16

17 Seller Revenue In which of the two auctions (first or second price) is the seller making more money? 17

18 Other auctions All-pay auctions Every bidder pays her bid Common value auctions Value = common part + error Winner s curse 18

19 Reserve Prices Adding a minimum reserve price can often increase revenue First-price Second-price Can significantly increase revenue 19

20 Exercise Second price auction with two bidders: Each bidder has value 5 or 10 with probability ½ Revenue: Revenue with reserve price R (> 5): Best reserve price? 20

21 HOMEWORK 1. Give the fastest algorithm to find, for any edge of a graph, the number of pairs of nodes whose shortest paths go through this node. (Extra: Use the algorithm to compute the fraction of the total number of shortest s-t paths that go through this edge, for a given pair s,t). 2. Give a polynomial time algorithm for finding the smallest affiliation network explaining a given social network edges, or show that it is NP-hard. 21

22 HOMEWORK CONTD 3. Exercise of the text on adding tolls in traffic networks 4. Exercise 10 from Chapter 9 (on entry price for auctions) 5. Exercise 11 from Chapter 10 (on matching markets) 22