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 incentive- compatible, 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!

Sponsored Search Auctions

Ad Auctions Generalized Second Price (GSP) – Google, Yahoo, Bing Bid on keywords – If the user query contains your keyword, your bid qualifies for the auction

GSP Auction Setting

GSP Auction

GSP Properties

Locally Envy Free Equilibrium