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CS6283 Topics in Computer Science IV: Computational Social Choice

CS6283 Topics in Computer Science IV: Computational Social Choice. Instructor: Yair Zick 2017. Introduction to Mechanism Design. Truthful Auctions and Bidding. Auctions Around Us. Why do we want truthful reporting?. Single Item Auctions. We have a single item for sale.

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CS6283 Topics in Computer Science IV: Computational Social Choice

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  1. CS6283 Topics in Computer Science IV: Computational Social Choice Instructor: YairZick 2017

  2. Introduction to Mechanism Design Truthful Auctions and Bidding

  3. Auctions Around Us

  4. Why do we want truthful reporting?

  5. Single Item Auctions We have a single item for sale. Each bidder values the item at . Seller can decide on a price. What are the outcomes?

  6. Single Item Auction Formats • English auction: • auctioneer sets a starting price • bidders take turn raising their bids • the person who makes the last bid wins and pays his bid • Japanese auction: • auctioneer sets a starting price and then starts raising it • a bidder can drop out, and cannot return once he dropped • the bidder who stays in last gets the object, pays the current price

  7. Single Item Auction Formats, Continued • Dutch auction: • auctioneer sets a (high) starting price and then starts lowering it • the auction ends when some bidder accepts the price • used in the Amsterdam flower market • Sealed-bid auction: • all bidders simultaneously submit their bid • the highest bidder gets the item and pays.... • his bid (first-price auction) • 2nd highest bid (second-price, or Vickrey, auction)

  8. English Auction • Suppose your value for the object is , the current price is , and the minimum bid increment is • It is rational to bid if and only , and your bid should be • If , and you end up winning, you will pay more than the object is worth to you. • If you bid more than , but no one else was willing to pay more than , you pay more than is necessary to win.

  9. English Auction, Dynamics . The auction starts at . While , all bidders are submitting bids. At , player stops bidding. At , player stops bidding. If player was the one to bid , she wins and pays . If player was the one to bid , player bids and wins. Winning bid is either or .

  10. Japanese Auction, Dynamics • The auction starts at • At , player drops out • At , player drops out • Player wins and pays • Communication: • English auction: 50 messages • Japanese auction: 2 messages

  11. Vickrey Auction • All bidders submit bids simultaneously in sealed envelopes, • The highest bidder wins and pays the second highest price • Strategic game • players (bidders) • actions: bids (continuous action space) • payoff: if a player values the object at and the 2nd highest bid is , her payoff is • if she gets the object • if she does not get the object

  12. In a Vickreyauction, truthful bidding is a dominant strategy

  13. Proof: • suppose your value is • suppose other players’ bids are • Case 1: • if you bid , you win and pay ; payoff is • if you bid , you lose; payoff is .

  14. Proof: • suppose your value is • suppose other players’ bids are • Case 2: • if you bid , you win and pay ; payoff is • if you bid , you lose; payoff is .

  15. Is Truthful Bidding a Strictly Dominant Strategy? • is an equilibrium in dominant strategies. • is also a NE • auctioneer makes no profit • is also a NE • Player 1 gets the object and pays nothing • if player 2 increases his bid so as to beat player 1, she will end up paying at least 70, so she cannot increase her profit

  16. Are 1st Price Auctions Truthful?

  17. Multi Unit Auctions We have a multiple, identical items for sale. Each bidder wants one item; values the item at . Assume that Seller can decide on prices. What are the outcomes?

  18. Multi Unit Auctions

  19. Multi Unit Auctions We have a multiple, different items for sale. Each bidder wants one item; values item at . Seller can decide on prices. What are the outcomes?

  20. Multi Unit Auctions

  21. How Complex Should we Be to Get ‘Good’ Equilibria?

  22. The Revelation Principle Let be a mechanism with a (very complicated) query model; then there exists a mechanism whose inputs are users’ valuations, and whose outputs are exactly like those of .

  23. Revelation Principle in Practice

  24. In VCG mechanisms, truthful reporting is a dominant strategy.

  25. Total social welfare Does not depend on ’s report Utility of player when she reports truthfully:

  26. Further Reading • Basic Mechanism Design • Chapters 9 and 10 of Algorithmic Game Theory by Nisan et al. • Further reading: • Combinatorial Auctions • Approximate Mechanism Design

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