Game Theory

The strategy in daily life

Foundation

• The three winners for Nobel prize at economy field in 1994

• John F. Nash

• Reinhard Selten

• John Harsanyi

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

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

The studies of the games

• Zero-sum game theory

• Non zero-sum game theory

• Prisoner's Dilemma

• Simultaneous-move game

- Nash Equilibrium

• Dynamic game

Zero-sum game theory

• All sides can win or lose

• One person's victory simultaneously heralds the opponent's defeat

• Examples： poker card

Prisoner’s Dilemma

• A and B are two arrested thieves• The policeman tells A:1. “If you conceal and the other confesses, you

will be taken into custody for nine weeks .”2. “If you conceal and the other conceals, both of

you will be taken into custody for one week.”3. “If you confess and the other confesses, both

of you will be taken into custody for six weeks.”

4. “If you confess and the other conceals, you will be released.”

B

conceals confesses

A

conceals -1， -1 -9， 0

confesses 0， -9 -6， -6

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

From A’s view

A confesses: -6 ---better• B confesses

A conceals: -9

A confesses: 0 ---better• B conceals

A conceals: -1• Whether B confesses or conceals, A’s confe

ssion is the best policy.

Nash Equilibrium

•Selling ice shavings on the beach

The picture is represented the beach

0 1/4 1/2 3/4 1

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