### 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

**years.**

^{5}### 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.