1. cs234r Markets for Networks and Crowds B RENDAN L UCIER, M ICROSOFT R ESEARCH NE N ICOLE I MMORLICA, M ICROSOFT R ESEARCH NE

2. Lecture 9: Babaioff, Lucier, Nisan, and Paes Leme. On the Efficiency of the Walrasian Mechanism. Preliminary version in Economics and Computation (EC), 2014.

3. RESOURCE ALLOCATION I have a collection of indivisible items to sell. How should I sell them? Run an AuctionPost Prices

4. RESOURCE ALLOCATION I have a collection of indivisible items to sell. How should I sell them? “When goods are not standardized or when the market clearing prices are highly unstable, posted prices work poorly, and auctions are usually preferred.” - Paul Milgrom

5. MODEL

6. Supermarket – price-taking buyers Small markets – bargaining/haggling

7. Model: proxy bidding (Hurwicz 72) Agents declare valuations to a central mechanism Mechanism computes a Walrasian equilibrium for the reported preferences This mechanism is approximately strategyproof in sufficiently large & well-behaved markets. [Rustichini, Satterthwaite, Williams], [Roberts, Postlewaite], [Jackson, Manelli], [Azevedo, Budish] Q. What happens without large-market assumptions? WALRASIAN MECHANISM

8. Example WALRASIAN MECHANISM 1.1 224 Prices

9. Example WALRASIAN MECHANISM 1.1 224 Prices

10. Example WALRASIAN MECHANISM 1.1 224 Prices 202

11. Example WALRASIAN MECHANISM 1.1 224 00 Prices 202 demand reduction increases utility!

12. “Such behavior, which is the essence of bargaining, may lead to impasse that delays or lessens the gains from trade.” [Rustichini, Satterthwaite, Williams] WALRASIAN MECHANISM

13. Example WALRASIAN MECHANISM 1.1 224 00 Prices 202 Welfare ratio of 4/(2+1.1)=1.21. How bad can it be? demand reduction increases utility!

14. WALRASIAN MECHANISM

16. Informal Discussion: Take-away: When individuals have market power, it is not necessarily efficient to compute “market prices.” But it will be approximately efficient in some cases. Questions: For what markets is this mechanism reasonable? Could we sell FCC spectrum this way? What does it mean for a market to be “large?”