ECO290E Game Theory
Lecture 1: Introduction and Motivation
What is Game Theory?
Game theory is a field of Mathematics,
analyzing strategically inter-dependent
situations (or strategic situations) in which the
outcome of your actions depends also on the
actions of others.
⇒
Are mathematical models helpful?
⇒
Is strategic thinking really important?
Are Mathematical Models Helpful?
Physical phenomena - Natural Science
Follow consistent patters, i.e., natural laws
We cannot ask objects for the reason behind the event.
⇒ Mathematical models are necessary.
Economic (Social) phenomena - Social Science
Each person acts anyway she wants.
She can explain why she took a specific action.
⇒ No mathematical model is needed (?)
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.
Advantages of Math Models
Mathematical model can be served as a
1.
Guideline for fact-finding.
2.
Device of checking consistency between different
explanations.
3.
Common language shared by researchers.
Two approaches are both important: not
substitute, but complement.
Traditional Economics
Traditionally, economics
focused (almost) only
on the ideal market
economy, called
“perfectly competitive
market.”
Supply and demand is
the main tool.
Is Strategic Thinking Relevant?
In demand-supply analysis, the market outcome is
derived by the intersection of the demand curve and
the supply curve.
There is NO strategic inter-dependence in its
framework.
Q: What’s the underlying assumption?
A: Each economic agent is a “price-taker .”
Need for Game Theory
Q: Can most of problems in Economics analyzed by
supply-demand? A: NO!
von Neumann and
Morgenstern (1944)
“We need essentially new mathematical theory to
solve variety of problems in social sciences.”
Strategic Thinking: Example
Example: Google vs. Apple
Google’s (optimal) action depends on how Google
predicts the Apple’s action.
Apple’s action depends on how Apple predicts the Google’s action.
Google’s action depends on how Google predicts
how Apple predicts the Google’s action.
Google’s action depends on how Google predicts
how Apple predicts how Google predicts the Apple’s
action.
and so on… (this is called “infinite regress”)
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.
Fields Transformed by Game Theory
How does economy function if market is immature or does not exist?
⇒ Economic History, Development Economics
How does government (politician, bureaucrat) behave?
⇒ Political Economics
What’s going on inside private companies?
⇒ Organizational Economics
How to compare different types of market economy?
⇒ Comparative Institutional Analysis
Discovery by vNM
Any social problem can be formalized as a
“game” which consists of three elements:
Players: relevant agents i=1,2,…,N
i’s Strategy: possible choice of actions
i’s Payoff: utility for each possible action profile
Q: What’s the solution of games?
⇒
Von Neumann and Morgenstern failed to
A Beautiful Mind Discovered It!
John Nash (1950) established THE solution concept:
In (Nash) equilibrium, no one can benefit if she unilaterally changes her action.
The solution always exists.
John Harsanyi and Reinhard Selten significantly extended Nash equilibrium.
Triggered a thousands of applications of game theory.
⇒ Revolution by game theory!
Impact of Nash
“Soon after Nash’s work, game-theoretic models began
to be used in economic theory and political science,
and psychologists began studying how human subjects
behave in experimental games. In the 1970s game
theory was first used as a tool in evolutionary biology .
Subsequently, game-theoretic methods have come to
dominate microeconomic theory and are used also in
many other fields of economics and a wide range of
other social and behavioral sciences.” (from an
introduction to Game Theory (Osborne, 2004), page 2)
Three Fathers of Game Theory
Revolution Continues…
- Novel Prize for Game Theory since 1994
1996: Mirrlees, Vickrey
for their fundamental contributions to the economic theory of incentives under asymmetric information.
2001: Akerlof, Spence, Stiglitz
for their analyses of markets with asymmetric information.
2005: Aumann, Schelling
for having enhanced our understanding of conflict and cooperation through game-theory analysis.
2007: Hurwicz, Maskin, Myerson
The Last Year (2012) As Well
- Roth and Shapley for Market Design!
Market Design: from Theory to Practice
Applying new insights in microeconomic theory (game theory), market design tries to (re-)design actual markets and to fix market failures.
Experiments and simulations are used to check the performance. => Engineering
New mechanisms proposed by economists are implemented in real world. => Practical
[1] Spectrum Auctions
The first spectrum auction was operated in New Zealand in 1990, which was not so successful.
How can we appropriately sell spectrum licenses with potentially highly interdependent values?
In 1994, on the advice of economists, the U.S. Federal Communications Commission (FCC) started the
simultaneous multi-rounds ascending-bid (SMRA) auctions:
“The Greatest Auction Ever” (NY Times, 1995)
The British spectrum auction of 2000 designed by economists raised about 22.5billion pounds!
⇒ Market design changes industry structure.
[2] Markets for New Doctors
In each year, around 20000 new American doctors are
assigned to their hospitals via a centralized clearinghouse: National Resident Matching Program (NRMP).
Both students and hospitals submit their ranking orders, and assignments are made based on these reported
preferences.
This matching program was re-designed in 1998: (student- proposing) deferred acceptance algorithm.
Japan (2003-) and some regions in UK adapted the same resident matching program.
[3] Kidney Exchange
The shortage of transplantable kidneys is a serious problem: 11000 transplants / 70000+ waiting list.
A live-donor may want to donate her kidney to a particular patient, say to her husband, but often it is biologically incompatible.
Economists provided a way to resolve this mismatch problem in 2004: pooling incompatible patient-donor pairs and appropriately exchange their partners.
This kidney exchange mechanism is implemented in New England, and started to save patients’ life!
Market design saves lives.
[4] School Choice Program
School choice, which enables students to choose public schools beyond their residence area, is implemented in many countries.
Its idea has broad public support, but how to operate school choice remains actively debated.
Based on economists’ advise, NYC and Boston redesigned their mechanisms in 2003 and 2005.
Both practically and theoretically important issues remain to be solved: frontier of market design!
Market design improves education.
Real Life Applications
Auction Design
Radio spectrum
Treasury bills
AdWords (Google)
Matching Mechanisms
Medical residency
Kidney exchange
Public school choice
There are Many Success Stories!
Use “Money”
Radio spectrum
Treasury bills
AdWords (Google)
No “Money”
Medical residency
Kidney exchange
Public school choice
Applications Deserve Nobel Prize!
Auction design
Radio spectrum
Treasury bills
AdWords (Google)
Matching mechanisms
Medical residency
Kidney exchange
Public school choice
Further Exercises
List up strategically interdependent situations from daily problems you encounter.
Survey the academic achievements made by Nobel laureates listed on slide 15.
Check out research fields other than Economics in which game theory is used or applied.
