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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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Presentation Transcript
outline
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
Games with Simultaneous Moves
  • Simultaneous moves?

Strategy vs. action

  • Discrete/Continuous strategy
slide4
Games in normal (strategic) form.
  • Games Table/ Game Matrix/ Payoff Table
nash equilibrium
Nash Equilibrium
  • What is Equilibrium?
  • Cell-by-cell-inspection or enumeration
  • Best Response Analysis
slide8
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.
slide10
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

dominance
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)
slide12
(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.
slide13
Both (all) Players Have Dominant Strategies
  • One Player has a Dominant Strategy
three players
Three Players

TALIA chooses C

TALIA chooses NC

three players17
Three Players

TALIA chooses D

TALIA chooses ND

multiple equilibria in pure strategies
Multiple Equilibria in Pure Strategies
  • Coordination Games
  • Battle of the Sexes
slide19
Focal Point
  • Convergence of expectation
  • Assurance Games
no equilibrium in pure strategies
No Equilibrium in Pure Strategies
  • Rock-Paper-Scissors
  • N.E exists in mixed Strategies
slide21
Homework, Ch4
  • question 3, 6, 11, and 12(a & b)
tree form into a strategic form
Tree form into a strategic form

L

(3, 1)

U

(2, 2)

R

2

1

D

L

(1, 3)

R

(4, 1)

2