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