WELCOMEWELCOME TOTO ECONOMICSECONOMICS S- S-10501050::

SSTRATEGY, TRATEGY, CCONFLICT & ONFLICT & CCOOPERATIONOOPERATION

Summer 2008Tu, Th, 6-8:30

Sever 214Instructor: Robert Neugeboren

neugebor@fas.harvard.edu

Teaching Assistant: Rajiv Shankar rshankar@fas.harvard.edu

Website: http://www.isites.harvard.edu/k35467

Office Hours: W 3-4 51 Brattle St.

Today’s Agenda

• Go Over Syllabus–Objectives–Requirements–Readings–Topics

• What is Game Theory?• An Experiment• Next Time

Description

Game theory is the study of interdependent decision-making. In the early days of the cold war, game theory was used to analyze an emerging nuclear arms race; today, it has applications in economics, psychology, politics, the law and other fields. In this course, we will explore the “strategic way of thinking” as developed by game theorists over the past sixty years. Special attention will be paid to the move from zero-sum to nonzero-sum game theory.

Description

Students will learn the basic solution concepts of game theory -- including minimax and Nash equilibrium -- by playing and analyzing games in class, and then we will take up some game-theoretic applications in negotiation settings: the strategic use of threats, bluffs and promises. We will also study the repeated prisoner’s dilemma and investigate how cooperative behavior may emerge in a population of rational egoists.

Description

This problematic -- “the evolution of cooperation” -- extends from economics and political science to biology and artificial intelligence, and it presents a host of interesting challenges for both theoretical and applied research. Finally, we will consider the changing context for the development of game theory today, in particular, the need to achieve international cooperation on economic and environmental issues.

Objectives

The course has two main objective: to introduce students to the fundamental problems and solution concepts of noncooperative game theory; and to provide an historical perspective on its development, from the analysis of military conflicts to contemporary applications in economics and other fields. No special mathematical preparation is required.

Requirements

10% Section. Include new material.

20% Problem Sets. Due in class.30% Midterm Exam. In class: July 17. 40% Final Exam. August 12, 3 hrs.

Graduate Credit: 12-15 page term paper, due August 8.

Readings

Axelrod, The Evolution of Cooperation (1984).

Gibbons, Game Theory for Applied Economists (1992).

Poundstone, Prisoner’s Dilemma (1992).

Rapoport, Two Person Game Theory (1966)

Schelling, The Strategy of Conflict (1960).

Available at the Coop.

Additional Readings denoted by an asterisk (*) are available

on e-Reserves: http://ereserves.harvard.edu/spring.html

Readings

READINGS RECOMMENDED FOR FURTHER INTEREST

Binmore, Game Theory and the Social Contract, Volume II (1998).

Gibbons, A Primer on Game Theory (199?):

Kreps, Game Theory and Economic Modelling (1994).

Raiffa, The Art and Science of Negotiation (1982).

Course Policies

Academic Honesty

Harvard takes matters of academic honesty very seriously. While you may discuss assignments with your classmates and others, make sure any written material you submit is your own work. Use of old course materials, including exams and problem sets from online sources, is prohibited. You should consult the Official Register of the Harvard Summer School and the website http://www.summer.harvard.edu to familiarize yourself with the possible serious consequences of academic dishonesty.

Course Policies

Late Policy

There will be 4 problem sets assigned roughly every other week, due in section. You can submit 1 problem set late, but only until the answer key is posted.

Topics

UNIT I OVERVIEW AND HISTORYUNIT II THE BASIC THEORY

July 17 MIDTERM

UNIT III THE EVOLUTION OF COOPERATIONUNIT IV THINKING ABOUT THINKING Aug 12 FINAL EXAM

Topics

UNIT I OVERVIEW AND HISTORY

6/24 Introduction: What is Game Theory?6/26 Von Neumann and the Bomb.

The Science of International Strategy.7/1 The Logic of Indeterminate Situations.

7/4 HOLIDAY

Topics

UNIT II THE BASIC THEORY

7/8 Zerosum and Nonzerosum Games.

7/10 Nash Equilibrium: properties and problems.

7/15 Bargaining Problems and (some) Solutions.

Ultimatum and Dictator Games.

7/17 MIDTERM

Topics

UNIT III THE EVOLUTION OF COOPERATION

7/22 The Evolution of International Cooperation?Repeated Games: the Folk Theorem.

7/24 Evolutionary Games.A Tournament.

7/29 How to Promote Cooperation.Unit Review.

Topics

UNIT IV THINKING ABOUT THINKING

7/31 Playing Fair.Behavioral Game Theory.

8/5 Learning Models.The Evolution of International Cooperation?

8/7 Conclusions and Review.8/12 FINAL EXAM

UNIT I: Overview & History

• Introduction: What is Game Theory?• Von Neumann and the Bomb• The Science of International Strategy• Logic of Indeterminate Situations

6/24

What is Game Theory?

• Games of Strategy v. Games of Chance• The Strategic Way of Thinking• An Experiment• Next Time

If we confine our study to the theory of strategy, we seriously restrict ourselves by the assumption of rational behavior – not just of intelligent behavior, but of behavior motivated by a conscious calculation of advantages, a calculation that in turn is based on an explicit and internally consistent value system (Schelling, 1960, p. 4).

What is Game Theory?

What is Game Theory?

Normative theories tell us how a rational player will behave.

Descriptive theories tell us how real people actually behave.

Prescriptive theories offer advice on how real people should behave.

What is Game Theory?

Rationality: The assumption that a player will attempt to maximize her expected payoff from playing a game.

Strategy: A complete plan of action for every possible decision in a game.

Equilibrium: A state of the game in which no player has an incentive to change her strategy.

Definitions (preliminary)

Rationality: choosing the best MEANS to attain given ENDS.

MEANS ENDSActions Preferences(x, y) A > BB > A where: x = buy A A = B

y = buy B

What is Game Theory?

Rationality: choosing the best MEANS to attain given ENDS.

MEANS ENDSActions Preferences(x, y) A > BB > A where: x = buy A A = B

y = buy B

What is Game Theory?

?

What is Game Theory?N = 1 n

MONOPOLY ? PERFECT COMPETITION

Price setter ? Price taker Inefficient ? Efficient

Game theory confronts this problem at the heart of economic theory: a theory of rational behavior when people interact directly, and prices are determined endogenously.

Games of Chance

Buy Don’t Buy

(1000) (-1) (0) (0)

Player 1

Chance

You are offered a fair gamble to purchase a lottery ticket that pays $1000, if your number is drawn. The ticket costs $1.

The chance of your number being chosen is fixed by statistical laws.

Games of Strategy

Buy Don’t Buy

(1000,-1000) (-1,1) (0,0) (0,0)

Player 1

Player 2

Player 2 chooses the winning number.

What are Player 2’s payoffs?

• Games of strategy require at least two players.

• Players choose strategies and get payoffs. Chance is not a player!

• In games of chance, uncertainty is probabilistic, random, subject to statistical regularities.

• In games of strategy, uncertainty is not random; rather it results from the choice of another strategic actor.

• Thus, game theory is to games of strategy as probability theory is to games of chance.

Games of Strategy

Games of Chance Games of StrategyExamples Roulette Chess, PokerPlayers 1 > 2Uncertainty Random Strategic (non-random)

Probability theory Game theory (Statistics)

• Thus, game theory is to games of strategy as probability theory is to games of chance.

Games of Strategy

The Strategic Way of Thinking

The parametrically rational actor treats his environment as a constant, whereas the strategically rational actor takes account of the fact that the environment is made up of other actors and that he is part of their environment, and that they know this, etc. In a community of parametrically rational actors each will believe that he is the only one whose behavior is variable, and that all others are parameters for his decision problem (Elster, 1979, p. 18).

The Strategic Way of Thinking

In the strategic or game-theoretic mode of interaction, each actor has to take account of the intentions of all other actors, including the fact that their intentions are based upon their expectations concerning his own (Elster, 1979, p. 18).

An ExperimentA) Smallest Value of X

7 6 5 4 3 2 1Your 7 1.30 1.10 0.90 0.70 0.50 0.30 0.10Choice 6 - 1.20 1.00 0.80 0.60 0.40 0.20of 5 - - 1.10 0.90 0.70 0.50 0.30X 4 - - - 1.00 0.80 0.60 0.40

3 - - - - 0.90 0.70 0.50 2 - - - - - 0.80 0.60 1 - - - - - - 0.70

Your Payoff = 0.10(Your Choice of X) - 0.20(Your Choice of X - Smallest X) + 0.60

(Source: Van Huyck, Battalio and Beil, 1990)

An ExperimentA) Smallest Value of X

7 6 5 4 3 2 1

Your 7 1.30 1.10 0.90 0.70 0.50 0.30 0.10

Choice 6 - 1.20 1.00 0.80 0.60 0.40 0.20

of 5 - - 1.10 0.90 0.70 0.50 0.30

X 4 - - - 1.00 0.80 0.60 0.40

3 - - - - 0.90 0.70 0.50

2 - - - - - 0.80 0.60

1 - - - - - - 0.70

7 is the efficient choice

An ExperimentA) Smallest Value of X

7 6 5 4 3 2 1

Your 7 1.30 1.10 0.90 0.70 0.50 0.30 0.10

Choice 6 - 1.20 1.00 0.80 0.60 0.40 0.20

of 5 - - 1.10 0.90 0.70 0.50 0.30

X 4 - - - 1.00 0.80 0.60 0.40

3 - - - - 0.90 0.70 0.50

2 - - - - - 0.80 0.60

1 - - - - - - 0.70

1 is the secure (or prudent) choice

An ExperimentA) Smallest Value of X

7 6 5 4 3 2 1

Your 7 1.30 1.10 0.90 0.70 0.50 0.30 0.10

Choice 6 - 1.20 1.00 0.80 0.60 0.40 0.20

of 5 - - 1.10 0.90 0.70 0.50 0.30

X 4 - - - 1.00 0.80 0.60 0.40

3 - - - - 0.90 0.70 0.50

2 - - - - - 0.80 0.60

1 - - - - - - 0.70

Multiple equilibria COORDINATION PROBLEM

An Experiment

What happened when we played the game?

What would happen if communication were permitted?

Is there a rational way to play?

Next Time

6/26 Von Neumann and the Bomb

Poundstone: 1-166.

Schelling, Strategy and Conflict: 3-52; 207-254

Hayward, Military Decision & Game Theory: 365-385 *