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An Introduction to Game Theory

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Growing Up with Game Theory. Rock, Paper, Scissors. Tic-Tac-Toe. Survivor ... Other Types of Games. Zero Sum Game. Tic-Tac-Toe. Winner = 1, Loser = -1, Tie = 0 ... – PowerPoint PPT presentation

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Title: An Introduction to Game Theory


1
An Introduction toGame Theory
  • Kelly Bielak
  • 12/8/05

2
Growing Up with Game Theory
  • Rock, Paper, Scissors
  • Tic-Tac-Toe
  • Survivor
  • Weakest Link

3
What is Game Theory?
  • A multi-agent decision problem
  • There are numerous people contending for limited
    rewards
  • They have to make certain moves on which their
    payoff depends
  • Have to follow certain rules
  • Each player is supposed to behave rationally-
    trying to maximize profit irrespective to what
    other players are doing
  • Economics, sociology, political science, etc.

4
Two Branches
  • Non Co-operative
  • Players work independently without assuming
    anything about what other players are doing
  • Co-operative
  • Players co-operate with one another
  • Extensive Form Players make their moves in
    turns, there is more than one move in a game, and
    each move is known to all players
  • Normal Form One shot, players make simultaneous
    moves

5
But What Exactly is a Game?
  • Set of players
  • Set of rules
  • Set of strategies
  • Moves players use during game
  • A rational player would chose strategies to
    maximize payoff
  • Set of outcomes
  • Payoff

6
Example Coin Matching Game
  • Set of Players- P1 P2
  • Set of Rules- Each player chooses H or T
    independently. P1 wins if both selections are the
    same, otherwise P2 wins
  • Set Strategies- Each can chose either H or T
  • Set of Outcomes- (H,H),(T,T)P1 wins
    (H,T),(T,H)P2 wins
  • Payoff- P1 wins or P2 winscan have set amounts
    for payoff
  • Your Turn!

7
Other Types of Games
  • Zero Sum Game
  • Tic-Tac-Toe
  • Winner 1, Loser -1, Tie 0
  • Constant Sum Game
  • Chess
  • Winner 1, Loser 0, Tie ½ each
  • Non Zero Sum Game
  • Prisoners Dilemma

8
Prisoners Dilemma
  • 2 players Prisoner 1 Prisoner 2
  • Each has 2 possible actions Confess or Dont
    Confess
  • Players chose actions simultaneously without
    knowing the action of the other
  • Payoff in prison years

9
Prisoners Dilemma
  • If both prisoners confess, each will be given a 5
    year sentence
  • If both prisoners Do Not confess, the police will
    be able to pin a part of the crime on both each
    will be given a 2 year sentence
  • If one confesses and the other does not, the
    confessor will make a deal with the police go
    free while the other goes to jail for 10 years

10
Your Turn!
  • Think of it this way
  • The goal is to figure out the other persons
    strategy use it to minimize your jail time (not
    screw the other person over)

11
Strategy Behind the Dilemma(For Prisoner 1)
  • If Prisoner 2 confesses
  • Confessing gives P1 5 years
  • Denying will give P1 10 years
  • Better for P1 to confess
  • If Prisoner 2 doesnt confess
  • Confessing frees P1
  • Denying will give P1 2 years
  • Again, its better for P1 to confess

12
For Those of You in Probability
  • P1 confesses with probability q
  • P1 assumes P2 would confess with
  • probability p
  • Therefore
  • 5pq 0xq(1-p) 10x(1-q)p 2(1-q)(1-p) qp
    q(4p1) years

13
Works Consulted
  • Introduction to Game Theory
  • Game Theory
  • What is Game Theory?
  • Games, Dilemmas, and Traps
  • Prisoners' Dilemma Interactive Game
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