哈佛博弈论讲义section1
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GOV 2005: Game Theory
Section 1
Alexis Diamond adiamond@fas.harvard.edu
.
Agenda
• What is game theory? • Exercise: convergence to equilibrium • Key terms and definitions • Formal theory: what Leo has to say about it • How do you do it (using formal theory) • Application: Alliance Formation • Final thoughts
The world of our constructs is therefore the desired island that is exempt from the flux of blind and aimless c. ausation.
Applying Formal Theory
• Goal (research question) • Story (model) • Formalization (abstraction) • Analysis (manipulation) • Solution (definition of equilibrium) • Translation (external and internal validity)
• Weakly dominant versus strongly (strictly dominant) strategies
Mixed Strategy
• Moves are chosen randomly from the set of pure strategies
• Every simultaneous move game has a Nash equilibrium in mixed strategies
.
Exercise: Moving to Equilibrium
i(si)ui(si,si)
siSi
# Player 1's
10 # Player 2's
20
# Playing Up
10 # Playing Left
20
Pl 1 Outcome
-8 Pl 2 Outcome
10
A Game in Normal Form
Three or Four Important Concepts
Beliefs: Probability distribution over strategies of other players
Dominant Strategy
• One best strategy no matter what your opponent does
We have absolutely certain or scientific knowledge only of those subjects of which we are the causes… The construction must be conscious construction; it is impossible to know a scientific truth without knowing at the same time that we have made it.
– One for every information set
• Equilibrium: a stability concept • Welfare • Pareto optimality: no. free lunch
Formal Theory: What’s it good for?
“We understand only what we make” --Leo Strauss
Example: Alliance Formation
Nash equilibrium: When each player is playing a best response to the strategie.s of the others
Key Terms and Definitions
• Normal form and extensive form • Nodes (initial, terminal) • Information sets • Strategy: complete contingent plan
wk.baidu.comPlayer 1 Up
Player 2
Left -8, 10
Right -10, 9
Down
7, 6
6, 5
Expected Value:
Avg payoff for pla. ying with prob distribution p, given others play strategies with prob distribution q
Game Theory is just one of several formal modeling approaches
General Equilibrium: interactions among many (infinite) agents, where any one agent’s actio.ns have no effect on other agents.
.
What Defines Game Theory?
Formal Analysis of Strategic Settings
• Mathematically precise • List of players • Complete description of allowable moves • Description of information • Specification of how actions cause outcomes • Specification of players’ preferences
Section 1
Alexis Diamond adiamond@fas.harvard.edu
.
Agenda
• What is game theory? • Exercise: convergence to equilibrium • Key terms and definitions • Formal theory: what Leo has to say about it • How do you do it (using formal theory) • Application: Alliance Formation • Final thoughts
The world of our constructs is therefore the desired island that is exempt from the flux of blind and aimless c. ausation.
Applying Formal Theory
• Goal (research question) • Story (model) • Formalization (abstraction) • Analysis (manipulation) • Solution (definition of equilibrium) • Translation (external and internal validity)
• Weakly dominant versus strongly (strictly dominant) strategies
Mixed Strategy
• Moves are chosen randomly from the set of pure strategies
• Every simultaneous move game has a Nash equilibrium in mixed strategies
.
Exercise: Moving to Equilibrium
i(si)ui(si,si)
siSi
# Player 1's
10 # Player 2's
20
# Playing Up
10 # Playing Left
20
Pl 1 Outcome
-8 Pl 2 Outcome
10
A Game in Normal Form
Three or Four Important Concepts
Beliefs: Probability distribution over strategies of other players
Dominant Strategy
• One best strategy no matter what your opponent does
We have absolutely certain or scientific knowledge only of those subjects of which we are the causes… The construction must be conscious construction; it is impossible to know a scientific truth without knowing at the same time that we have made it.
– One for every information set
• Equilibrium: a stability concept • Welfare • Pareto optimality: no. free lunch
Formal Theory: What’s it good for?
“We understand only what we make” --Leo Strauss
Example: Alliance Formation
Nash equilibrium: When each player is playing a best response to the strategie.s of the others
Key Terms and Definitions
• Normal form and extensive form • Nodes (initial, terminal) • Information sets • Strategy: complete contingent plan
wk.baidu.comPlayer 1 Up
Player 2
Left -8, 10
Right -10, 9
Down
7, 6
6, 5
Expected Value:
Avg payoff for pla. ying with prob distribution p, given others play strategies with prob distribution q
Game Theory is just one of several formal modeling approaches
General Equilibrium: interactions among many (infinite) agents, where any one agent’s actio.ns have no effect on other agents.
.
What Defines Game Theory?
Formal Analysis of Strategic Settings
• Mathematically precise • List of players • Complete description of allowable moves • Description of information • Specification of how actions cause outcomes • Specification of players’ preferences