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GAME THEORY MY PRESENTATION …

GAME THEORY MY PRESENTATION

Published in: Technology, Economy & Finance
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  • 1. GAME THEORY
  • 2. Outline What is game theory? History of game theory. Application of game theory. Key elements of game theory. Types of game. Nash Equilibrium(NB) Pure strategies and mixed strategies. 2 players Zero- sum game.
  • 3. Game theoryGame theoryi s the analysis of conflict and cooperationamong intelligent rational decision makers.A decision maker is said to be rational if he makesdecisions consistently in a pursuit of his own objectives.In a game, two or more individuals make decisions thatinuence each others expected utility.The decision makers are called the players.The decision objects of players are generally calledstrategies.
  • 4. Game theory uses two basic toolsModels offers two games.There is a variety of models that represent dierentscenarios that might show up in real-life situations-Solution concepts.Solution concepts are predictions about what rational intelligenplayers should play.
  • 5. History of game theory Von Neumann wrote a key paper in 1928 1944:”Theory of games and Economic Behaviour "by von Neumann and Morgenstern 1950:Nash invent concepts of Nash equilibrium Game theory booms after this…. 1944:Harsani,Nash and Selten win Nobel prize in economics for game theory work
  • 6. Application of Game Theory Mathematics  Psychology Computer science  Law Biology  Military Strategy Economics  Sports Political science  Game Playing International Relation Philosophy
  • 7. Key elements of a Game Players: Who is interacting? Strategies: What are their options? Payoffs: What are their incentives? Information: What do they work? Rationality: How do they think?
  • 8. Types of games Cooperative or non-cooperztive Zero sum and non –zero sum Simultaneous and sequential Perfect information and imperfect information Finite and Infinite Strategies
  • 9. Pure Strategies The upper value of the game is equel to the minimum of the maximum values in the columns The lower value of the game is equalto the maximum of the minimum values in the rows.
  • 10. An Example AB Y1 Y2 MinimumX1 10 6 6X2 -12 7 -12Maximum 10 6 6 7
  • 11. 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
  • 12. Nash Eqilibrium(NE) A player’s best strategy is that strategy that maximizes that player’s payoff(utility)’knowing the strategy’s of the other players.
  • 13. Penny Matching: Each of the two players has a penny. 2 players must simultaneously choose whwther to show the Head or the Tail. Both players know the following rules:  If two pennies match (both heads or both tails ) then players 2 wins payer1’s penny.  Otherwise,player 1 wins player 2’s penny Player 2 Head Tail Head -1 , 1 1 , -1 Player 1 Tail 1 , -1 -1 , 1
  • 14. Prisoner’s Dilemma No communication:  Strategies must be undertaken without the full knowledge of what the the other players (prisoners)will do. Players (prisoners) develop dominant strategies but are not necessarily the best one.
  • 15. Payoff Matrix for Prisoner’s Dilemma Ted Confess Not confess Confess Both get 5 years 1 year for Bill 10 years for tedBill 10 years for Bill Both get 3 years Not Confess 1 year for Ted
  • 16. An Example of Mixed Startegygame A B believes B doesn’t believe B A bluffs 1 0 A doesn’t bluff 0 0.5
  • 17. Nash Equilibrium This equilibrium occurswhen player’s strategy is optimal,knowing the strategy’s of the other player’s. A player’s best strategy is thet startegy that maximize that player’s payoff(utility), knowing the strategy’s of the other players. So when each player within a game follows their best strategy, a Nash Equilibrium will occur.

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