Mechanism Design Ruta Mehta Game design not video

Game design (not video games!) to achieve a desired goal, like fairness, social welfare

Lets Focus on Voting • -> Condorcet’s Paradox!

First Preference Majority • Tie between a and c

Gibbard-Satterthwaite Theorem: If a social choice function is incentivecompatible, where |A|>=3, then it is

Vickery Auction is IC (in DS) Proof on board

Open-Outcry Auctions • English Auction: Start with a low price and keep increasing until

Clarke Pivot Rule • Others welfare without i Others welfare with i

Pros and Cons of VCG • Best for bidders – Government auctions like road

Ad Auctions • Generalized Second Price (GSP) – Google, Yahoo, Bing • Bid on

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Mechanism Design Ruta Mehta

Game design (not video games!) to achieve a desired goal, like fairness, social welfare maximization, etc.

Widely Applicable

Lets Focus on Voting • -> Condorcet’s Paradox!

First Preference Majority • Tie between a and c

Borda Count •

In General: Social Choice •

Desired Properties of f •

Gibbard-Satterthwaite Theorem: If a social choice function is incentivecompatible, where |A|>=3, then it is dictatorship. “Field of Mechanism Design attempts escaping from this impossibility result using various modifications in the model. ”

Introducing Payment •

Auction • Not even IC

Vickery Auction is IC (in DS) Proof on board

Open-Outcry Auctions • English Auction: Start with a low price and keep increasing until only one buyer is interested. – Equivalent to Vickery auction! • Dutch Auction: Start with a very high price where no one is interested. Keep decreasing until someone gets interested. – Equivalent to first price auction!

Extensions? •

General Setting •

Example: Single Item Auction •

Vickery-Clarke-Groves Mechanism •

Properties of VCG Proof on board •

Clarke Pivot Rule • Others welfare without i Others welfare with i

Example: Single Item Auction •

Example: Multiunit Auction •

Example: Reverse Auction •

Example: Resource Allocation •

Example: Multi Item Auction •

Incentive Compatible •

Pros and Cons of VCG • Best for bidders – Government auctions like road contract, bandwidth allocation • May not be efficiently computable – Multi item auction • Worst for auctioneer – May get zero payment!