University of North Texas
Department of Political Science
Spring 1996
PSCI 6000
Game Theory
Instructor: David A. Leblang, Wooten 145; x2313; dleblang@unt.edu
Time & Location: Monday 2:00-5:00, Wooten 131
Office Hours: M 1:00-2:00, T 11:00-12:00, W 10:00-12:00, and by appointment
Description
“Game theory” can be defined as multiperson decision theory or as an approach to
understanding interdependent choice. Topics investigated from a game theoretic point of
view have traditionally included the use of threats and bluffs and punishments and
rewards. Over the last twenty years game theory has been used to explore the building of
reputations and the signaling of an unobservable type. Additional topics studied by game
theorists include bargaining and repeated interactions between actors.
This course introduces the student to game theory and to game theoretic modeling.
Emphasis is placed on developing a substantive understanding of the uses of game theory
in the social sciences. While game theory has been largely developed by mathematicians
and economists, the substantive applications in this course come from a variety of
disciplines in the social sciences including economics, political science, sociology and
law.
The goal of this course is to prepare the student to read, understand, and critique gametheoretic literature. A related goal is to provide a foundation upon which the student can
undertake further study and conduct research in game theory.
We will cover the following topics in this course: extensive and normal (strategic) form
games, Nash equilibrium and some of its refinements (e.g., subgame perfection, perfect
Bayesian equilibrium, sequential equilibrium), finitely and infinitely repeated games (folk
theorems), and games of imperfect information (e.g., signaling, adverse selection).
There are no formal prerequisites for this course. That being said, this course in entirely
self-contained; I assume no prior knowledge of game theory. However, to be successful,
the student should have some degree of mathematical sophistication: a willingness to
reason and interpret abstruse definitions literally and a tolerance for manipulating and
working through dense notation. The prerequisites for learning game theory were perhaps
best stated by Luce and Raiffa in 1957: “Certainly neither the calculus nor matrix algebra
are required, but neither will hinder, for probably the most important prerequisite is that
ill-defined quality: mathematical sophistication.”
Recent game theoretic work requires (at a minimum) a familiarity with probability theory,
mathematical expectation and basic calculus. We will have two or three additional
(“bonus”) classes to cover the basics of set theory, probability theory, Bayes’ theorem and
single variable calculus. These classes will be scheduled at a time convenient to all
participants. These additional classes are not optional; if you do not attend these classes
the probability that you will fully grasp the game-theoretic material will approach zero.
Requirements
1. Classroom Discussion: It is the student’s responsibility to be prepared to discuss the
information and claims found in the readings and to think about the related research
possibilities. Learning game theory (or any formal theory for that matter) is like studying
a foreign language: it is cumulative. You cannot understand equilibrium refinements, for
example, if you do not understand the concept of an equilibria. If you don’t ask questions
then I must assume that the material is clear. (10%).
2. Problem Sets: there will be four or five problem sets over the course of the semester.
These problem sets are very important for your understanding of the course material. I
fully expect that you will turn in all of the assignments; failure to do so will result in a
zero. Late assignments will not be accepted. (40%).
3. Article Review: you will select a game-theoretic article from any sub-field within
political science and write a review. This review will follow the style of book reviews in
the APSR. It should include a discussion of the contributions and limitations of the article
as well as proposed directions for future research. You should clear the article with me
before you begin to write your review. (15%) DUE: April 15.
4. Research Prospectus and Design: you will write a complete research design for
possible paper. In this design you will indicate: (i) the theoretical issue/problem/ question
that is of interest to you; (ii) the relevant (game-theoretic and non-game-theoretic)
literature that has addressed this question; (iii) your theoretical approach (e.g., your
hypothesis); (iv) the game-theoretic model you will employ; and (v) your expected
findings. (35%) DUE: Monday, May 6.
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The following have been ordered and should be available in the bookstore:
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Alt, James and Kenneth Shepsle (eds.). 1990. Perspectives on Positive Political
Economy. Cambridge: Cambridge University Press.
Baird, Douglas, et al. 1995. Game Theory and The Law. Cambridge: Harvard
Banks, Jeff and Eric Hanushek (eds.). 1995. Modern Political Economy. Cambridge:
Cambridge University Press.
Binmore, Ken. 1990. Fun and Games. New York: Heath.
Dixit, Avinash and Barry Nalebuff. 1989. Thinking Strategically. NY: WW Norton.
Gates, Scott and Brian Humes. Forthcoming. Games, Information, and Politics:
Applying Game Theoretic Models to Politics. Ann Arbor: University of Michigan
Press. [Manuscript available at the copy shop]
Hargreaves Heap, Shaun, et al. (eds.). 1992. The Theory of Choice: A Critical Guide.
Cambridge: Blackwell.
Kreps, David. 1990. A Course in Microeconomic Theory. Princeton: Princeton
University Press.
Morrow, James. 1994. Game Theory for Political Scientists. Princeton: Princeton
University Press.
Rasmusen, Eric. 1995. Games and Information, Second Edition. Cambridge:
Blackwell.
The required readings will be assigned from Dixit & Nalebuff, Gates & Humes, and
Rasmusen. These three books will serve as the core material for this course. Binmore
and Kreps provide more rigorous discussions of the material. Morrow is written for
political scientists; it is an excellent source of applications and bibliographic references.
Baird is a text that applies game theory to the study of legal issues. Alt & Shepsle and
Banks & Hanushek are collections of essays in the area of positive political economy;
these essays trace where positive political economy has been and where it is going.
Hargreaves Heap is a survey of choice theoretic models ranging from individual choice
to interdependent choice to collective choice. It also includes a very useful glossary.
You should also get your hands on a good probability and statistics text. Some
econometrics books have short chapters on probability theory. I recommend Amemiya,
Introduction to Statistics and Econometrics; Kmenta, Elements of Econometrics, Second
Edition; Hogg and Tanis, Probability and Statistical Inference, Fourth Edition; and
Freund and Simon, Modern Elementary Statistics, Eighth Edition.
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1.
Introduction
Overview and history of game theory; Rational choice theory, utility, risk, preferences;
Modeling competitive situations, rules of the game.
Required Reading
Rasmusen, Introduction, 1.1; Dixit & Nalebuff, Introduction, Ch 1.
Optional Material
Kreps, pp.3-14, 17-37, 71-86, 98-131, 355-63; Binmore, Introduction, pp.67-139; 146-74;
Morrow, Chs 1-2.
Background and Applications
Aldrich, John. 1993. “Rational Choice and Turnout,” American Journal of Political
Science, 37:246-78.
Riker, William. 1990. “Political Science and Rational Choice,” in Alt and Shepsle
(eds). Perspectives on Positive Political Economy. NY: Cambridge University Press.
Machina, Mark. 1987. “Choice Under Uncertainty: Problems Solved and Unsolved.”
Journal of Economic Perspectives, 1:121-54.
2.
Games in Normal/Strategic Form
2.1
Specifying a game; Dominant strategies: strong v. weak; Dominant strategy
equilibrium; Nash equilibrium.
Required Reading
Rasmusen, Chapter 1; Dixit & Nalebuff, Ch 3.
Optional Material
Kreps, pp. 376-380, 387-406; Morrow, chapter 4.
Background and Applications
Bates, Robert. 1983. “The Preservation of Order in Stateless Societies: A
Reinterpretation of Evans-Pritchard’s The Neur.” In Essays on the Political Economy
of Rural Africa. Berkeley: University of California Press.
Geddes, Barbara. 1991. “A Game Theoretic Model of Reform in Latin American
Democracies.” American Political Science Review 85:371-92.
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2.2
Mixed Strategies; Reaction curves; Probability theory, expectation, lotteries;
Interpretation, comparative static.
Required Reading
Rasmusen, 3.1-3.3; Dixit & Nalebuff, Ch. 7.
Optional Material
Kreps, pp.380-84, 387-406; Binmore, chapter 7; Morrow, chapter 4.
Background and Applications
Debreu, G. 1952. “A Social Equilibrium Existence Theorem.” Proceedings of the
National Academy of Sciences, 886-93.
2.3
Modeling strategies.
Required Reading
Gates and Humes, Chapter 3, pp.91-96; Baird, Chapter 1.
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Games in Extensive Form
3.1
Rules of the Game; Information (perfect, complete, etc.).
Required Reading
Rasmusen, 2.1-2.2; Kreps, pp.363-376; Dixit & Nalebuff, Ch 2.
Optional Material
Binmore, chapter 1; Morrow, chapter 3
Background and Applications
Przeworski, Adam. 1991. “Transitions to Democracy,” Chapter 2 in Democracy and
the Market: Political and Economic Reform in Eastern Europe and Latin America.
NY: Cambridge University Press.
Kuhn, H. 1953. “Extensive Games and the Problem of Information,” in H.W. Kuhn
and A.W. Tucker, eds. Contributions to the Theory of Games II. Princeton:
Princeton University Press.
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3.2
Backwards induction; Subgame perfection.
Required Reading
Rasmusen, 4.1-4.3; Dixit & Nalebuff, Ch. 6
Optional Material
Kreps, pp.417-425; Morrow, chapter 5.
Background and Applications
Baird, chapter 2
Zagare, Frank. 1990. “Rationality and Deterrence.” World Politics 42:238-60.
Reny, Philip. 1992. “Rationality in Extensive-Form Games.” Journal of Economic
Perspectives 6:103-118.
4.
Repeated Games
4.1
Rules; Discounting; Complete and symmetric information.
Required Reading
Rasmusen 4.5-4.6, Gates and Humes, chapter 4; Dixit & Nalebuff, ch 4.
Optional Material
Kreps, chapter 14; Morrow, chapter 9
Background and Applications
Rider, Robert. 1993. “War, Pillage, and Markets.” Public Choice 75:149-56.
Baird, chapter 5
4.2
Finitely repeated games, “Gang of Four” model, Axelrod’s Tournament.
Required Reading
Rasmusen, 5.1-5.3, 6.4-6.5
Optional Material
Kreps, chapter 14; Morrow, chapter 9
Background and Applications
Kreps, D., P. Milgrom, J. Roberts, and R. Wilson. 1982. “Rational Cooperation in the
Finitely Repeated Prisoners Dilemma,” Journal of Economic Theory 27:245-52.
Benoit, J.P and V. Krishna. 1985. “Finitely Repeated Games,” Econometrica 317-20.
Axelrod, Robert. 1984. The Evolution of Cooperation. NY: Basic Books.
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5.
Bayesian Equilibria.
Conditional probability and Bayes’ theorem; Updating beliefs; Perfect Bayesian
Equilibria; Behavioral strategies.
Required Reading
Rasmusen, 2.1-2.4; Morrow, chapter 6
Background and Applications
Geanakoplos, John. 1982. “Common Knowledge,” Journal of Economic Perspectives
6:53-82.
Kilgour, D. Marc and Frank C. Zagare. 1991. “Credibility, Uncertainty, and
Deterrence,” American Journal of Political Science 35:305-34.
Nalebuff, Barry. 1991. “Rational Deterrence in an Imperfect World. World Politics.
43:313-35.
6.
Perfect and Sequential Equilibrium.
Weak dominance; Trembling-hand perfect equilibria; Sequential equilibria.
Required Reading
Rasmusen, 6.1-6.3; Gates and Humes, chapter 5.
Optional Material
Kreps, pp.425-443; Morrow, chapter 7.
Background and Applications
Baird, chapter 3
Selten, R. 1975. “Reexamination of the Perfectness Concept for Equilibrium points in
Extensive Games.” International Journal of Game Theory 25-55
Kreps, D. And R. Wilson. 1982. “Sequential Equilibria.” Econometrica, 863-94.
7.
Asymmetric Information.
Complete v. Incomplete information; Out-of-equilibrium beliefs, restrictions on beliefs;
Cheap talk; Moral hazard, adverse selection, signaling; Pooling v. Separating.
Required Reading
Rasmusen, chapters 7-10; Gates and Humes, chapter 6.
Optional Material
Kreps, chapters 13, 16-17; Morrow, chapter 8; Baird, chapter 4.
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