Transcript ECO290E: Game Theory

ECO290E: Game Theory
Lecture 1
Introduction and Motivation
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What is Game Theory?
• Game theory is a field of Mathematics,
analyzing strategically inter-dependent
situations in which the outcome of your
actions depends also on the actions of
others.
 Are mathematical models helpful?
 Is strategic thinking really important?
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Are mathematical models
helpful?
Physical phenomena
• Follow natural laws.
• We cannot ask objects
for the reason behind
the event.
Economic phenomena
• Each person acts
anyway she wants.
• She can explain why
she took a specific
action.
 Mathematical models
are necessary.
 No mathematical model
is needed (?)
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Two alternative approaches
• Institutional knowledge: Look into the “facts”
in detail.
 Superficial knowledge alone cannot explain
economic movement.
• Economic Theory: Look for the “laws”
behind facts.
Q: What’s the fundamental economic law?
A: Each person acts for her own interest.
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Advantages of math models
Mathematical model can be served as a
• Guideline for fact-finding.
• Device of checking consistency
between different explanations.
• Common language shared by
researchers.
Two approaches are both important: not
substitute, but complement.
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Is strategic thinking
relevant?
• In price theory, the market outcome is
derived by the intersection of the demand
curve and the supply curve. (demand-supply
analysis)
• There is no strategic inter-dependence in its
framework.
Q: What’s the underlying assumption?
A: Each economic agent is a “price-taker.”
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The birth of Game Theory
Q: Are most of problems in Economics
indeed mere applications of
“constrained optimization”?
A: NO!
von Neumann and Morgenstern (1944)
“We need essentially new mathematical
theory to solve variety of problems in
social sciences.”
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Strategic Thinking: Example
Example: Nintendo vs. Sony
• Nintendo’s action depends on how Nintendo
predicts the Sony’s action.
• Nintendo’s action depends on how Nintendo
predicts how Sony predicts the Nintendo’s
action.
• Nintendo’s action depends on how Nintendo
predicts how Sony predicts how Nintendo
predicts the Sony’s action.
and so on…
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Revolution by Game Theory
• Game theory can solve the problem of
strategic inter-dependence by pinning down
how to predict other players’ action.
Therefore, game theory
• Provides us tools for analyzing important
economic phenomena beyond market
economy (with perfect competition).
• Enables us to compare different resource
allocation mechanisms.
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New Areas Pioneered by GT
• How does economy function if market is immature or
not existing?
 Economic History, Development Economics
• How do governments behave?
 Political Economics
• What’s going on inside private companies?
 Organizational Economics
• How to compare different types of market economy?
 Comparative Institutional Analysis
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Discovery by vN=M
• Any social problem can be formalized as a
“game,” consisting of three elements:
Players: i=1,2,…,N
i’s Strategy: si  Si
i’s Payoff:  i (s1 ,...,sN )
Q: What’s the solution of games?
 They failed to establish a general solution
concept…
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Nash Equilibrium
John Nash: “A Beautiful Mind” (movie)
• The solution of games must satisfy the
following criterion.
Nash equilibrium (mathematical definition)
s  ( s ,...,s )
*
*
1
*
N
i, si
 i ( s )   i ( s , si )
*
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i
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Interpretations of NE.
• No one can benefit if she unilaterally
changes her action from the original
Nash equilibrium.
 NE describes a stable situation.
• Everyone correctly predicts other
players’ actions and takes bestresponse against them.
 NE serves as a rational prediction.
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Rationality Question
Q: Does NE heavily depend on rationality of
players?
A: Not necessarily so.
Example: NE in Evolutionary Biology
Strategy = “phenotype” : a character of each
animal determined by its gene
Payoff = “fitness” : a number of the offspring
• NE is a stable situation reached not by
rationality but by evolutionary dynamics.
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Existence Question
Q: Does NE always exist?
A: Yes (in almost every cases).
Theorem (Nash, 1950)
“There exists at least one Nash
equilibrium in any finite games in which
the numbers of players and strategies
are both finite.”
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