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”.
⇒ 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.
Preferences need not be selfish, or materially based.
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.”
Every agent (consumer, firm, etc) reacts to market prices, not (directly) to other agents’ actions.
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.
It dramatically changed economics since 80’s!
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 individuals (also called “agents”)
Strategy: their possible choice of actions
Payoff: their utility for each possible action profile
Q: What’s the solution of games?
⇒
Von Neumann and Morgenstern failed to
establish a general solution concept…
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.”
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
for having laid the foundations of mechanism design theory.
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
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
Example: Prisoners ’ Dilemma
Two suspects are charged with a joint crime,
and are held separately by the police.
Each prisoner is told the following (assume
that a plea bargain is allowed):
If both confess, each receives 3 years imprisonment.
If neither confesses, both receive 1 year.
If one confesses and the other one does not, the former will be set free immediately (0 payoff) and the latter receives 5 years.
Prisoners’ Dilemma: Payoff Matrix
Here we set payoffs as (negative of) years.
Other numbers such that larger number shows better outcomes can express the same situations.
Player 2 Player 1
Silent Confess
Silent -1 -1
0 -5
Confess -5 0
-3 -3
How to Use (Read) Bi-Matrices
Any two players game (with finite number of
strategies) can be expressed as a bi-matrix, called payoff bi-matrix or payoff matrix.
The payoffs to the two players when a particular pair of strategies is chosen are given in the appropriate cell.
The payoff to the row player (player 1) is given first, followed by the payoff to the column player (player 2).
⇒ How can we solve this game?
Prisoners’ Dilemma: Analysis (1)
If the opponent (player 2) chooses Silent,
Playing Confess is better since 0 > -1. Player 2
Player 1
Silent Confess
Silent -1 -1
0 -5
Confess -5 0
-3 -3
Prisoners’ Dilemma: Analysis (2)
If the opponent (player 2) chooses Confess,
Playing Confess is better since -3 > -5. Player 2
Player 1
Silent Confess
Silent -1 -1
0 -5
Confess -5 0
-3 -3
Prisoners’ Dilemma: Analysis (3)
(Silent, Silent) looks mutually beneficial outcomes, though
Playing Confess is optimal regardless of other player’s choice!
Acting optimally (Confess, Confess) rends up realizing!!
Player 2 Player 1
Silent Confess
Silent -1 -1
0 -5
Confess -5 0
-3 -3
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.
Find a social problem which can be described as a Prisoner’s Dilemma.
