What is Game Theory all about? A Lecture Given at C.R.I. , Nov. 2 nd , 2004 Prof. Robert Aumann Center for Rationality Studies Hebrew University, Jerusalem Abstracted by Daphne Raban
Definition of Game Theory
Game theory provides a framework in which to model and analyze conflict and cooperation among different entities, each with its own goal
Applications of Game Theory
Game Theory in Economics: Examples
Auctions: Winner’s Curse, Second Price
Matchmaking and intern assignments
Competitive markets: Supply and Demand
Auctions: The Winner’s Curse
The winner’s curse stems from the fact that bids are distributed around their mean. Since the winner pays the highest bid, he/she pays the amount which is farthest above the mean bid. The true value is liable to be closer to the mean, so the winner is paying too much.
Auctions: Second Price
In traditional sealed bid auctions, bidders hesitate to bid their true valuation because they feel they may get the contract for less. William Vickrey won a Nobel Prize for suggesting that the highest bidder wins, and pays the second highest bid. This design elicits the true private value from bidders.
Example for the Use of Game Theory in Designing Auctions
The Spectrum Auction: The U.S. government was hoping to earn $0.5 billion.
Game theorists were retained to design the auction. As a result, in the first auction the U.S. government earned about $10 billion. In the second auction it earned about $50 billion.
Matchmaking and Hospital Interns
A stable matching requires that there should not exist two agents, each on a different side of the market, who prefer each other to the individual they have been paired with. In 1962 D. Gale and L. Shapley showed that in two-sided markets there always exists a stable matching.
The Gale-Shapley Theorem was used to explain the hospital intern matching algorithm developed in 1952, 10 years earlier! Now used in general to solve placement problems.
The theorem does not hold for “homosexual” matches - when the market has only one “side”.