Economics 1050: Strategy & Conflict in Spring 2017

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Game theory is a study of interdependent decision-making, evolving from analyzing nuclear arms race during the cold war to having diverse applications today. This course delves into strategic thinking through game theory, exploring solution concepts like Nash equilibrium and minimax, negotiation tactics, and the emergence of cooperation in game settings. Moreover, it addresses the evolution of cooperation across various disciplines and discusses the impact of behavioral game theory. Join this course to delve into the realm of strategic decision-making!

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WELCOME TO ECONOMICS 1050: STRATEGY, CONFLICT & COOPERATION Spring 2017 Tu, Th 2:30-4 Harvard 102 Instructor: Robert Neugeboren neugebor@fas.harvard.edu Office Hours: W 3-4 51 Brattle St, Rm 219 Sections: TBA TF: Mauricio Fernandez Duque duque@fas.harvard.edu Website: https://canvas.harvard.edu/courses/21475

Thomas Schelling (1921-2016) Thomas Schelling was an American economist; PhD, Harvard, 1948; joined the faculty in 1956; cofounded HKS; taught Econ 1030: Strategy and Conflict (1975-88?). He was awarded the 2005 Nobel Prize in Economics (shared with Robert Aumann) for "having enhanced our understanding of cooperation through analysis". conflict game and theory Schelling in 2007

Todays Agenda Go Over Syllabus Objectives Requirements Policies 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, business, politics, law, biology, and other fields. In this course, we will explore the strategic way of thinking as developed by game theorists over the past eighty 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 negotiation settings: the strategic use of threats, bluffs and promises. We will also study the repeated prisoner s dilemma game and investigate how cooperative behavior may emerge in a population of rational egoists. applications in

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. We will consider the changing context for the development of game theory today, in particular, the need to cooperation on economic and environmental issues. achieve international

Description Finally, we will discuss behavioral game theory, a relatively new field incorporating methods and insights from experimental economics psychology. and cognitive

Objectives The course has two main objectives: 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% Participation: 20% Problem Sets: 30% Midterm Exam: 40% Final Exam: Attendance is required. 4, every 2-3 weeks. In class, March 9. 3 hours, TBA.

Participation Participation by all students is in lecture and section 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.

Problem Sets There will be 4 problem sets assigned roughly every other week, due at the startof section. Each problem set will be graded on a 10 point scale and will count for 5% of your final grade. Late problem sets will not be accepted (except with notification from your RD).

Course Policies Problem Sets: Discussion and the exchange of ideas are essential to doing academic work. For assignments in this course, you are encouraged to consult with your classmates as you work on problem sets. However, after discussions with peers, make sure that you can work through the problem yourself and ensure that any answers you submit for evaluation are the result of your own efforts. In addition, you must cite any books, articles, websites, lectures, etc. that have helped you with your work using appropriate citation practices. Similarly, you must list the names of students with whom you have collaborated on problem sets.

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 Academic Integrity and Academic Dishonesty in the Harvard College Handbook for Students to familiarize yourself with consequences of academic dishonesty. the possible serious

Website The course website is a very useful place for you to visit: https://canvas.harvard.edu/courses/21475 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, dropboxes to submit assignments, links to interesting sites, and other useful resources.

Readings Axelrod, Gintis, Poundstone, Prisoner s Dilemma (1992). Rapoport, Two-Person Game Theory (1966). Schelling, The Strategy of Conflict (1960). -- Choice and Consequence (1984) The Evolution of Cooperation (1984). Game Theory Evolving (2000). Available at the Coop (and elsewhere) Additional Readings are available on the course website.

Readings READINGS RECOMMENDED FOR FURTHER INTEREST Binmore, Dutta, Hargreaves-Heap & Varoufakis. Game Theory: A Critical Introduction (1995). Kreps, Game Theory & Economic Modeling (1994). Raiffa, The Art & Science of Negotiation (1982). Game Theory & Social Contract, Vol II (1998). Strategies & Games (1999).

Topics UNIT I UNIT II THE BASIC THEORY OVERVIEW AND HISTORY March 9 MIDTERM UNIT III THE EVOLUTION OF COOPERATION UNIT IV BEYOND HOMO ECONOMICUS May ?? FINAL EXAM

Topics UNIT I OVERVIEW AND HISTORY Introduction: What is Game Theory? Von Neumann and the Bomb The Science of International Strategy The Logic of Indeterminate Situations

Topics UNIT II 3/9 THE BASIC THEORY Zerosum Games Nonzerosum Games Nash Equilibrium and Subgame Perfection Bargaining Problems and (some) Solutions Review MIDTERM SPRING BREAK

Topics UNIT III THE EVOLUTION OF COOPERATION The Tragedy of the Commons Repeated Games: the Folk Theorem Evolutionary Game Theory A Tournament Beyond Tit for Tat How to Promote Cooperation Unit Review

Topics BEYOND HOMO ECONOMICUS UNIT IV Schelling s Critique Behavioral Game Theory Social Preferences Experimental Economics Learning Models Evolution in Biological & Natural Systems Conclusions and Review 5/?? FINAL EXAM

UNIT I: Overview & History Introduction: What is Game Theory? Von Neumann and the Bomb The Science of International Strategy The Logic of Indeterminate Situations 1/24

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

What is Game Theory? If we confine our study to the theory of strategy, we seriously restrict 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 (Schelling, 1960, p. 4). ourselves by the value system

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? Definitions (preliminary) Rationality: The assumption that a player will attempt to maximize her expected payoff from playing a game.

What is Game Theory? Definitions (preliminary) 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.

What is Game Theory? Definitions (preliminary) 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.

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

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

What is Game Theory? PERFECT N = MONOPOLY ? 1 n COMPETITION Price setter ? Inefficient ? Price taker 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 Player 1 You are offered a fair gamble to purchase a lottery ticket that pays $1000, if your number is drawn. The ticket costs $1. Buy Don t Buy Chance (1000) (-1) (0) (0)

Games of Chance Player 1 You are offered a fair gamble to purchase a lottery ticket that pays $1000, if your number is drawn. The ticket costs $1. Buy Don t Buy Chance The chance of your number being chosen is fixed by statistical laws. (1000) (-1) (0) (0)

Games of Strategy Player 1 Player 2 chooses the winning number. Buy Don t Buy Player 2 (1000) (-1) (0) (0)

Games of Strategy Player 1 Player 2 chooses the winning number. Buy Don t Buy Player 2 What are Player 2 s payoffs? (1000,-1000) (-1,1) (0,0) (0,0)

Games of Strategy Games of strategy require at least two players. Players choose strategies and get payoffs. Chance is not a player!

Games of Strategy 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.

Games of Strategy 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 Strategy Examples Roulette Players 1 Uncertainty Random Probability theory (Statistics) Chess, Poker > 2 Strategic (non-random) Game theory Thus, game theory is to games of strategy as probability theory is to games of chance.

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 Experiment A) Your Choice 6 of X Smallest Value of X 5 4 0.90 0.70 1.00 0.80 1.10 0.90 - 1.00 - - - - - - 7 7 1.30 - - - - - - 6 1.10 1.20 - - - - - 2 0.30 0.40 0.50 0.60 0.70 0.80 - 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 3 0.50 0.60 0.70 0.80 0.90 - - 5 4 3 2 1 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 Experiment A) Your Choice 6 of X Smallest Value of X 5 4 0.90 0.70 1.00 0.80 1.10 0.90 - 1.00 - - - - - - 7 7 1.30 - - - - - - 6 1.10 1.20 - - - - - 2 0.30 0.40 0.50 0.60 0.70 0.80 - 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 3 0.50 0.60 0.70 0.80 0.90 - - 5 4 3 2 1 7 is the efficient choice

An Experiment A) Your Choice 6 of X Smallest Value of X 5 4 0.90 0.70 1.00 0.80 1.10 0.90 - 1.00 - - - - - - 7 7 1.30 - - - - - - 6 1.10 1.20 - - - - - 2 0.30 0.40 0.50 0.60 0.70 0.80 - 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 3 0.50 0.60 0.70 0.80 0.90 - - 5 4 3 2 1 1 is the secure (or prudent) choice

An Experiment A) Your Choice 6 of X Smallest Value of X 5 4 0.90 0.70 1.00 0.80 1.10 0.90 - 1.00 - - - - - - 7 7 1.30 - - - - - - 6 1.10 1.20 - - - - - 2 0.30 0.40 0.50 0.60 0.70 0.80 - 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 3 0.50 0.60 0.70 0.80 0.90 - - 5 4 3 2 1 Multiple equilibria COORDINATION PROBLEM