aumann_20041102

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aumann_20041102

  1. 1. 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
  2. 2. Definition of Game Theory <ul><li>Game theory provides a framework in which to model and analyze conflict and cooperation among different entities, each with its own goal </li></ul>
  3. 3. Applications of Game Theory <ul><li>Mathematics </li></ul><ul><li>Computer Science </li></ul><ul><li>Biology </li></ul><ul><li>Economics </li></ul><ul><li>Political Science </li></ul><ul><li>International Relations </li></ul><ul><li>Philosophy </li></ul><ul><li>Psychology </li></ul><ul><li>Law </li></ul><ul><li>Military Strategy </li></ul><ul><li>Management </li></ul><ul><li>Sports </li></ul><ul><li>Game Playing </li></ul><ul><li>Talmud </li></ul>
  4. 4. Game Theory in Economics: Examples <ul><li>Auctions: Winner’s Curse, Second Price </li></ul><ul><li>Bargaining: </li></ul><ul><ul><li>Strikes </li></ul></ul><ul><ul><li>Blackmailer’s paradox </li></ul></ul><ul><ul><li>Holiness </li></ul></ul><ul><ul><li>Commerce </li></ul></ul><ul><li>Matchmaking and intern assignments </li></ul><ul><li>Competitive markets: Supply and Demand </li></ul><ul><li>Bankruptcy </li></ul>
  5. 5. Auctions: The Winner’s Curse <ul><li>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. </li></ul>
  6. 6. Auctions: Second Price <ul><li>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. </li></ul>
  7. 7. Example for the Use of Game Theory in Designing Auctions <ul><li>The Spectrum Auction: The U.S. government was hoping to earn $0.5 billion. </li></ul><ul><li>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. </li></ul>
  8. 8. Matchmaking and Hospital Interns <ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>The theorem does not hold for “homosexual” matches - when the market has only one “side”. </li></ul>

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