哈佛博弈论讲义section1

Example: Alliance Formation
• 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
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.
Player 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
Three or Four Important Concepts
Beliefs: Probability distribution over strategies of other players
Dominant Strategy no matter what your opponent does
GOV 2005: Game Theory
Section 1
Alexis Diamond adiamond@
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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
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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
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
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
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)
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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