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Simplification Duals Expressiveness

Simplification Duals Expressiveness. By Scott Kominers And Lukens Orthwein. Why Simplify?. Computational Complexity Eliminating “Bad” Equilibria Unsophisticated Buyers Lazy Participants. Milgrom’s Simplification Thm . Milgrom’s Simplification Thm . Tractable Simplifications.

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Simplification Duals Expressiveness

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  1. Simplification Duals Expressiveness By Scott Kominers And Lukens Orthwein

  2. Why Simplify? • Computational Complexity • Eliminating “Bad” Equilibria • Unsophisticated Buyers • Lazy Participants

  3. Milgrom’s Simplification Thm.

  4. Milgrom’s Simplification Thm.

  5. Tractable Simplifications

  6. Simplified Search Auctions Why they’re desirable • Computational Complexity • Server Load (many keywords per second) • Eliminating “Bad” Equilibria • Low Revenue Equilibria • Unsophisticated Buyers • CS 286r Class (e.g. David Parkes) • Lazy Participants • See above

  7. Bad Equilibria in Search Auct.’s • Vickrey Auction: • Zero Revenue • Repeated Second Price Auction: • Zero Revenue! Anything Strange Here?

  8. Simplification to the Rescue! • Simplified Vickrey Auction: • Single bid from each buyer • Auctioneer computes bids for all positions • Generalized Second Price Auction: • Single bid from each buyer • Mechanism ranks buyers based on the bids and allocates accordingly w/ Second Price Auction rules Revenue!

  9. Package Auctions Why they’re desirable • Computational Complexity • HUGE domain (2n packages) • Eliminating “Bad” Equilibria • Inefficient Equilibria • Unsophisticated Buyers • Don’t know full preference set • Lazy Participants • Don’t care to express full preference set

  10. Simplified Package Auctions

  11. Affine Approximation Mechanisms Anything Strange Here?

  12. Thoughts? • Theory vs. Practice • Are Some of These Results Coincidental? • How Would You Sell Treasury Bills?

  13. Expressiveness in Mechanisms • What is Expressiveness? • The impact vector represents the effect your action could have on outcomes if you can express it

  14. Maximum Impact Dimension • The most buttons other agents can give you in order to allow you to affect the outcome of the mechanism. Anything Strange Here???

  15. Shatterable Outcome Dimension • Given a system with a set of rules, how many possible different outcomes can an agent effect? How about here?

  16. What is the Main Result? • Efficiency Benefits • Upper bound on efficiency is strictly monotonic with expressiveness • So what happens in equilibrium? • No idea... ?

  17. Tradeoffs Between Simplification and Expressiveness • Revenue vs. Efficiency • Tractability vs. Generality • Uncertainty vs. Certainty • What is the true nature of your customer? • Are we encouraging or discouraging entry?

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