Gov 2005, Formal Political Theory I Fall 2013

Wed 10AM-12 Noon Room K 031 Note: September 25th will be swapped with section(s) or rescheduled.

Game theory is now used widely in political science to analyze strategic interactions in many different settings. Each of the sub-fields, to differing degrees, has seen game theoretic concepts enter its vocabulary, and students entering the profession will need to understand the potential and limits of game theory. This course aims to give students a basic understanding of the fundamental concepts of game theory, and how these concepts have been applied to the study of political phenomena. Students will leave the course with a working knowledge of games of complete information, to the point where they can write down a model, solve it, and state some of the model’s empirical implications. Students will also have an introductory knowledge of games of incomplete information. Because an important component of game theory in political science and political economy is the analysis of substantive political phenomena, we will cover illustrative examples each week in combination with methodological developments. The political and economic phenomena that we will examine include legislative rules, nuclear deterrence, electoral competition, and imperfect markets. The purpose of these examples is not to offer a complete review of the literature. Rather, the examples are employed to provide students with the ability to analyze strategic situations and evaluate existing models in the field. This class requires careful reasoning and logic. Although many of the tools used in this course are mathematical in nature, there is no formal mathematical prerequisite. We will use basic calculus and probability theory, and if you do not have a strong background in these subjects you will have to brush up.

Reading Materials There are two required texts for the class: (1) Gibbons, Robert. 1992. Game Theory for Applied Economists. Princeton: Princeton University Press. (2) Osborne, Martin J. 2004. An Introduction to Game Theory. New York: Oxford University Press.

Requirements (1) Problem Sets. There will be weekly problem sets. These are worth 40% of your grade. While we encourage you to work in groups, you have to state who you collaborate with

1 and you cannot collaborate with the same person directly or indirectly more than 50% of the problem sets. (2) Final Exam. There will be a comprehensive final exam. The final will be an in-class exam based on the lessons of the problem sets. It is worth 30% of your grade. (3) Paper. There will be a paper due at the end of the term but that you will build on it throughout the course. You have to pick an qualitative/empirical paper or some idea you want to explore and the assignment consists on modeling its core argument over the course. There will be partial submission deadlines. It is worth 30% of your grade.

Weekly Outline (approximate)

I. Games of Complete Information

Week 1. Normal Form Games I Concepts: dominant strategies, Nash equilibrium in pure strategies, Nash equilibrium in mixed strategies) Applications: prisoners’ dilemma, battle of the sexes, matching pennies, chicken Gibbons, chapter 1 Osborne, chapter 2

Week 2. Normal Form Games II Applications (on continuous strategy spaces): duopoly, spatial electoral competition Gibbons, chapter 1 Osborne, chapters 2-4

Week 3. Normal Form Games III Applications (more than two players): oligopoly, electoral completion with three parties, tragedy of the commons Gibbons, chapter 1 Osborne, chapters 2-4

Week 4. Normal Form Games IV Applications (dominant strategies, more than two players, continuous strategy spaces): resource allocation, rent-seeking/ lobbying, duel, "truel." Martin Shubik. 1985. Game Theory in the Social Sciences: Concepts and Solutions. Vol. 1. MIT Press Esteban, Joan and Debraj Ray (1999). "Collective Action and the Group Size Paradox." The American Political Science Review, 95(3): 663-672.

Week 5. Extensive Form Games I Concepts: backwards induction, subgame perfect equilibrium Applications: legislative rules, Stackelberg duopoly, centipede, bank runs, principal- agent model , labor tournament Gibbons, chapter 2 Osborne, chapter 5-7

Week 6. Extensive Form Games II Applications: 2-player sequential bargaining, bargaining in legislatures Gibbons, chapter 2 Osborne, chapter 16

Week 7. Extensive Form Games III Applications: sophisticated voting and agenda control Morrow, chapter 5 Osborne, chapter 6-7

Week 8. Repeated Games Concepts: finitely repeated games, infinitely repeated games Applications: development of cooperation, overlapping generations Gibbons, chapter 2 Osborne, chapter 14

Avinash Dixit, Gene M. Grossman, and Faruk Gul. 2000. "The Dynamics of Political Compromise." Journal of Political Economy 108(3):531-568

II. Games of Incomplete Information

Week 9. Normal Form Games Concepts: Bayesian Nash equilibrium Applications: battle of the sexes again, auctions, the revelation principle Gibbons, chapter 3 Osborne, chapter 9

Week 10. Extensive Form Games I Applications: signaling games Gibbons, chapter 4 Osborne, chapter 10

Week 11. Extensive Form Games II Applications: cheap talk, informational role of committees Gibbons, chapter 4 Osborne, chapter 10

Week 12. Extensive Form Games II Applications: nuclear deterrence Gibbons, chapter 4 Osborne, chapter 10

Week 13. TBD.