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Abbas Keramati ( Assistant Professor)   University of Tehran – MBA Fall 2008 Game Theory Quantitative Analysis for Decisio...
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Game Theory Presentation

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Game Theory Presentation

  1. 1. Abbas Keramati ( Assistant Professor) University of Tehran – MBA Fall 2008 Game Theory Quantitative Analysis for Decision Making M.Ghotbi M.Pajhouh Niya
  2. 2. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Outline <ul><li>What is Game Theory? </li></ul><ul><li>History of Game Theory </li></ul><ul><li>Applications of Game Theory </li></ul><ul><li>Key Elements of a game </li></ul><ul><li>Types of games </li></ul><ul><li>Nash Equilibrium (NE) </li></ul><ul><li>Pure Strategies & Mixed Strategies </li></ul><ul><li>2players Zero-Sum games </li></ul>
  3. 3. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG What is Game Theory? <ul><li>In strategic games, agents choose strategies that will maximize their return, given the strategies the other agents choose. </li></ul><ul><li>The mathematics of human interactions </li></ul>
  4. 4. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG History of Game Theory <ul><li>von Neumann wrote a key paper in 1928 </li></ul><ul><li>1944: “ Theory of Games and Economic Behavior” by von Neumann and Morgenstern </li></ul><ul><li>1950: Nash invents concept of Nash equilibrium </li></ul><ul><li>Game theory booms after this… </li></ul><ul><li>1994: Harsanyi , Nash , and Selten win Nobel Prize in economics for game theory work </li></ul>
  5. 5. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG <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>Applications of Game Theory
  6. 6. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Key Elements of a game <ul><li>Players : Who is interacting? </li></ul><ul><li>Strategies : What are their options? </li></ul><ul><li>Payoffs : What are their incentives? </li></ul><ul><li>Information : What do they know? </li></ul><ul><li>Rationality : How do they think? </li></ul>
  7. 7. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Types of games <ul><li>Cooperative or non-cooperative </li></ul><ul><li>Zero sum and non-zero sum </li></ul><ul><li>Simultaneous and sequential </li></ul><ul><li>Perfect information and imperfect information </li></ul><ul><li>Finite & Infinite Strategies </li></ul>
  8. 8. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Pure Strategies <ul><li>The upper value of the game is equal to the minimum of the maximum values in the columns. </li></ul><ul><li>The lower value of the game is equal to the maximum of the minimum values in the rows. </li></ul>
  9. 9. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG An Example: -12 7 -12 X2 7 6 Y2 6 7 10 Maximum 6 10 X1 Minimum Y1 A B
  10. 10. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Mixed Strategies A mixed strategy game exists when there is no saddle point. Each player will then optimize their expected gain by determining the percent of time to use each strategy.
  11. 11. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Nash Equilibrium (NE) A player’s best strategy is that strategy that maximizes that player’s payoff (utility), knowing the strategy's of the other players.
  12. 12. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG 2-players Zero-Sum games Player 1 Player 2 <ul><li>Penny Matching: </li></ul><ul><li>Each of the two players has a penny. </li></ul><ul><li>Two players must simultaneously choose whether </li></ul><ul><li>to show the Head or the Tail. </li></ul><ul><li>Both players know the following rules: </li></ul><ul><ul><li>-If two pennies match (both heads or both </li></ul></ul><ul><ul><li>tails) then player 2 wins player 1’s penny. </li></ul></ul><ul><ul><li>-Otherwise, player 1 wins player 2’s penny. </li></ul></ul>-1 , 1 1 , -1 1 , -1 -1 , 1 Tail Head Tail Head
  13. 13. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Prisoner’s Dilemma <ul><li>No communication: </li></ul><ul><li>- Strategies must be undertaken without </li></ul><ul><li>the full knowledge of what the other </li></ul><ul><li>players (prisoners) will do. </li></ul><ul><li>Players (prisoners) develop dominant strategies but are not necessarily the best one. </li></ul>
  14. 14. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Ted Confess Not Confess Confess Bill Not Confess Payoff Matrix for Prisoner’s Dilemma Both get 3 years 10 years for Bill 1 year for Ted 1 year for Bill 10 years for Ted Both get 5 years
  15. 15. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG An Example of Mixed Strategy game 0.5 0 A doesn’t bluff 0 B doesn’t believe 1 A bluffs B believes A B
  16. 16. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Now let’s Play This Game Pirate Game A B D C E
  17. 17. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Nash’s Equilibrium <ul><li>This equilibrium occurs when each player’s strategy is optimal, knowing the strategy's of the other players. </li></ul><ul><li>A player’s best strategy is that strategy that maximizes that player’s payoff (utility), knowing the strategy's of the other players. </li></ul><ul><li>So when each player within a game follows their best strategy, a Nash equilibrium will occur. </li></ul>
  18. 18. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Definition: Nash Equilibrium Given others’ choices, player i cannot be better-off if she deviates from s i *
  19. 19. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG Nash’s Equilibrium cont.: Bayesian Nash Equilibrium <ul><li>The Nash Equilibrium of the imperfect-information game </li></ul><ul><ul><li>A Bayesian Equilibrium is a set of strategies such that each player is playing a best response, given a particular set of beliefs about the move by nature. </li></ul></ul><ul><ul><li>All players have the same prior beliefs about the probability distribution on nature’s moves. </li></ul></ul><ul><ul><ul><li>So for example, all players think the odds of player 1 being of a particular type is p , and the probability of her being the other type is 1-p </li></ul></ul></ul>
  20. 20. Title <ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul><ul><li>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. </li></ul>DGDG <ul><li>Dixit and Nalebuff: Thinking Strategically </li></ul><ul><li>Dutta: </li></ul><ul><li>Strategies and Games: Theory and Practice </li></ul><ul><li>www.gametheory.net </li></ul>Refrences

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