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Games with Simultaneous Moves I :Discrete Strategies

Games with Simultaneous Moves I :Discrete Strategies. Outline. Games with simultaneous moves Nash Equilibrium Dominance Minimax in Zero-sum Game Three Players Multiple/Zero Equilibria in pure strategies Tree Forms into Strategic Forms. Games with Simultaneous Moves. Simultaneous moves?

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Games with Simultaneous Moves I :Discrete Strategies

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  1. Games with Simultaneous Moves I:Discrete Strategies

  2. Outline • Games with simultaneous moves • Nash Equilibrium • Dominance • Minimax in Zero-sum Game • Three Players • Multiple/Zero Equilibria in pure strategies • Tree Forms into Strategic Forms

  3. Games with Simultaneous Moves • Simultaneous moves? Strategy vs. action • Discrete/Continuous strategy

  4. Games in normal (strategic) form. • Games Table/ Game Matrix/ Payoff Table

  5. Zero-sum Game

  6. Nash Equilibrium • What is Equilibrium? • Cell-by-cell-inspection or enumeration • Best Response Analysis

  7. The N.E is (Low, Middle) →(5, 4) • A Nash Equilibrium in a game is a list of strategies, one for each player, such that no player can get a better payoff by switching to some other strategy that is available to her while all the other players adhere to the strategies specified for them in the list.

  8. A N.E. does not have to be jointly best for the players. EX: Prisoner’s dilemma

  9. Nash Equilibrium as a system of beliefs • Nash Equilibrium is a set of strategies, such that (1)each player has correct beliefs about the strategies of the others (2)the strategy of each is the best for herself, given her beliefs about the strategies of the others

  10. Dominance • Dominant strategy is an action clearly best for a player, no matter what the others might be doing. • “Confess” is a dominant strategy for the husband, while “Confess” is also a dominant strategy for the wife. NE: (Confess, Confess) →(10yr, 10yr)

  11. (A,B,…..) are strategies for Player 1. • A is a dominant strategy for Player 1. • A dominates B/C/D…. • B/C/D… is a dominated strategy for Player 1.

  12. Both (all) Players Have Dominant Strategies • One Player has a Dominant Strategy

  13. Successive (Iterated) Elimination of Dominated Strategies

  14. MiniMax Method for Zero-Sum Games • MiniMax/Maximin

  15. Three Players TALIA chooses C TALIA chooses NC

  16. Three Players TALIA chooses D TALIA chooses ND

  17. Multiple Equilibria in Pure Strategies • Coordination Games • Battle of the Sexes

  18. Focal Point • Convergence of expectation • Assurance Games

  19. No Equilibrium in Pure Strategies • Rock-Paper-Scissors • N.E exists in mixed Strategies

  20. Homework, Ch4 • question 3, 6, 11, and 12(a & b)

  21. Tree form into a strategic form L (3, 1) U (2, 2) R 2 1 D L (1, 3) R (4, 1) 2

  22. Minimax/Maximin vs. Nash Equilibrium Revisited

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