Game Theory

1
Game Theory
The strategy in daily life
2
Foundation

• The three winners for Nobel prize at economy
  field in 1994
• John F. Nash
• Reinhard Selten
• John Harsanyi

3
What is Game Theory

• Game theory is a branch of mathematics
• A tactic thinking in daily life
• By tactic guessing, players can find out the best
  strategy and the largest pay-off for themselves

4
The three basic elements of games

• Two or more players, each player has two or more
  strategy to select
• The outcome depends on chosen strategies by
  players
• Players have different preferences toward the
  outcomes, which influence players strategies

5
The studies of the games

• Zero-sum game theory
• Non zero-sum game theory
• Prisoner's Dilemma
• Simultaneous-move game
• - Nash Equilibrium
• Dynamic game

6
Zero-sum game theory

• All sides can win or lose
• One person's victory simultaneously heralds the
  opponent's defeat
• Examplespoker card

7
Prisoners Dilemma

• A and B are two arrested thieves
• The policeman tells A
• If you conceal and the other confesses, you will
  be taken into custody for nine weeks .
• If you conceal and the other conceals, both of
  you will be taken into custody for one week.
• If you confess and the other confesses, both of
  you will be taken into custody for six weeks.
• If you confess and the other conceals, you will
  be released.

8
B B
conceals confesses
A conceals -1,-1 -9,0
A confesses 0,-9 -6,-6
9
To the sum benefit of A and B

• A conceals and B conceals -2 weeks
• A conceals and B confesses -9 weeks
• A confesses and B conceals -9 weeks
• A confesses and B confesses -12 weeks
• Both A and B concealment is the best policy

10
From As view

• A confesses -6
  ---better
• B confesses
• A conceals -9
• A confesses 0
  ---better
• B conceals
• A conceals -1
• Whether B confesses or conceals, As confession
  is the best policy.

11
Nash Equilibrium

• Selling ice shavings on the beach
• The picture is represented the beach

0
1/4
1/2
3/4
1
12

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