1. WELCOME TO ECONOMICS 1040 : S TRATEGY, C ONFLICT & C OOPERATION WELCOME TO ECONOMICS 1040 : S TRATEGY, C ONFLICT & C OOPERATION Spring 2007 W 7:35-9:35 Emerson 108 Instructor: Robert Neugeboren neugebor@fas.harvard.edu Teaching Fellow: Rajiv Shankar rshankar@fas.harvard.edu Website: http://www.courses.fas.harvard.edu/~ext21946/ Office Hours: W 3-4 51 Brattle St Sections: Tu 6:30-7:30 or 7:30-8:30

2. Today’s Agenda Go Over Syllabus –Objectives –Requirements –Readings –Topics What is Game Theory? An Experiment Next Time

3. 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.

4. 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.

5. 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.

6. 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.

7. Requirements 10% Section. Include new material. 20% Problem Sets. Due in class. 30% Midterm Exam. In class: March 14. 40% Final Exam. May 23.

8. Readings Axelrod,The Evolution of Cooperation (1984). Gibbons,Game Theory for Applied Economists (1992). Hargreaves-Heap & Varoufakis. Game Theory: A Critical Introduction (1995). Poundstone, Prisoner’s Dilemma (1992). Rapoport, Two-Person Game Theory (1966). Schelling, The Strategy of Conflict (1960). Available at the Coop (and elsewhere) Additional Readings denoted by an asterisk (*) are available on e-Reserves: http://ereserves.harvard.edu/spring.html http://ereserves.harvard.edu/spring.html

9. 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).

10. 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 Extension School and the website http://www.extension.harvard.edu to familiarize yourself with the possible serious consequences of academic dishonesty.http://www.extension.harvard.edu

11. Problem Sets There will be 4 problem sets assigned roughly every other week, due at the beginning of class. You can submit 1 problem set late for half-credit, but only until the answer key is posted.

12. Sections Attendance at sections is mandatory, and missed sections or tardiness may reduce your section grade. Participation by all students is strongly encouraged. Sections will be especially helpful in preparing for problem sets and reviewing for exams. The quality of your section experience depends heavily on the involvement of other students. As such, fostering a supportive, cooperative environment will be essential. Part of your participation grade will be based on your contribution to the learning environment in the classroom.

13. Website The course website is a very useful place for you to visit: www.courses.fas.harvard.edu/ext/21946.www.courses.fas.harvard.edu/ext/21946 All official course announcements (e.g., deadlines, class cancellations, exam notices, etc.) will appear on the homepage, and all assignments and answer keys will be posted there. There is also a discussion section, practice problems, additional readings, links to interesting sites, and other useful resources.

14. Topics UNIT IOVERVIEW AND HISTORY UNIT IITHE BASIC THEORY March 14 MIDTERM UNIT IIITHE EVOLUTION OF COOPERATION UNIT IVTHINKING ABOUT THINKING May 23 FINAL EXAM

15. Topics UNIT I OVERVIEW AND HISTORY 1/31Introduction: What is Game Theory? 2/7Von Neumann and the Bomb. The Science of International Strategy. 2/14The Logic of Indeterminate Situations. 7/4 HOLIDAY

16. Topics UNIT II THE BASIC THEORY 2/21Zerosum and Nonzerosum Games. 2/28Nash Equilibrium: properties and problems. 3/7Bargaining Problems and (some) Solutions. Ultimatum and Dictator Games. 3/14 MIDTERM

17. Topics UNIT III THE EVOLUTION OF COOPERATION 3/21The Evolution of International Cooperation? Repeated Games: the Folk Theorem. 4/4Evolutionary Games. A Tournament. 4/11How to Promote Cooperation. Unit Review.

18. Topics UNIT IV THINKING ABOUT THINKING 4/18Playing Fair. Behavioral Game Theory. 4/25Learning Models. Conclusions and Review. 5/2 The Evolution of International Cooperation? 5/9Conclusions and Review. 5/23 FINAL EXAM

19. UNIT I:Overview & History Introduction: What is Game Theory? Von Neumann and the Bomb The Science of International Strategy Logic of Indeterminate Situations 1/31

20. What is Game Theory? Games of Strategy v. Games of Chance The Strategic Way of Thinking An Experiment Next Time

21. 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?

22. 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.

23. 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)

24. 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)

25. 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)

26. Rationality: choosing the best MEANS to attain given ENDS. MEANSENDS Actions Preferences (x, y)A > B B > A where: x = buy AA = B y = buy B What is Game Theory?

27. Rationality: choosing the best MEANS to attain given ENDS. MEANSENDS Actions Preferences (x, y)A > B B > A where: x = buy AA = B y = buy B What is Game Theory? ?

28. 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.

29. 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.

30. 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.

31. Games of Strategy Buy Don’t Buy (1000) (-1) (0) (0) Player 1 Player 2 Player 2 chooses the winning number.

32. 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?

33. 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

34. 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

35. 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

36. Games of Chance Games of Strategy Examples Roulette Chess, Poker Players 1> 2 Uncertainty 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

37. 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).

38. 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).

39. An Experiment A) Smallest Value of X 7654321 Your 71.301.100.900.700.50 0.300.10 Choice 6 -1.201.000.800.600.400.20 of 5 - -1.100.900.700.500.30 X 4 - - -1.000.800.600.40 3 - - - -0.900.700.50 2 - - - - -0.800.60 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)

40. An Experiment A) Smallest Value of X 7654321 Your 71.301.100.900.700.50 0.300.10 Choice 6 -1.201.000.800.600.400.20 of 5 - -1.100.900.700.500.30 X 4 - - -1.000.800.600.40 3 - - - -0.900.700.50 2 - - - - -0.800.60 1 - - - - - -0.70 7 is the efficient choice

41. An Experiment A) Smallest Value of X 7654321 Your 71.301.100.900.700.50 0.300.10 Choice 6 -1.201.000.800.600.400.20 of 5 - -1.100.900.700.500.30 X 4 - - -1.000.800.600.40 3 - - - -0.900.700.50 2 - - - - -0.800.60 1 - - - - - -0.70 1 is the secure (or prudent) choice

42. An Experiment A) Smallest Value of X 7654321 Your 71.301.100.900.700.50 0.300.10 Choice 6 -1.201.000.800.600.400.20 of 5 - -1.100.900.700.500.30 X 4 - - -1.000.800.600.40 3 - - - -0.900.700.50 2 - - - - -0.800.60 1 - - - - - -0.70 Multiple equilibria COORDINATION PROBLEM

43. An Experiment What happened when we played the game? What would happen if communication were permitted? Is there a rational way to play?

44. Next Time 2/7 Von Neumann and the Bomb Poundstone: 1-166. Schelling, Strategy and Conflict: 3-52; 207-254 Hayward, Military Decision & Game Theory: 365-385 *