This course is designed with two aims in mind: First, to introduce students to the basic concepts and tools of game theory. Second, to demonstrate how formal models can be used in social science. Emphasis is placed on understanding the intuition and logic of game theory and its application in the social sciences. Students finishing this course should be in a position to read and evaluate the current game theoretic literature in political science.
The course starts with basic utility theory. From this platform, classical game theoretic ideas are developed. Having established the rudimentary concepts, these principals are applied in political science settings. I intend to develop the game theory and its substantive applications side by side. Different substantive areas are used to motivate different game theoretic concepts. The course covers many, although not all, of the recent development in non-cooperative game theory.
The course consists of a combination of lectures, and problem solving
sessions. In addition to class problems, regular homework problems will
be assigned. These problems will typically relate to the current topic
and so need to be completed in a timely fashion. These problem sets make
up 50% of the final grade. There will be a final take home exam and a mid
term.
The course concentrates on the intuition behind game theoretic models.
Despite this emphasis, some mathematics is required. Students contemplating
this class should, at a minimum, be comfortable with linear algebra and
elementary statistics. A knowledge of basic calculus is helpful but not
essential.
There is one required textbook: Morrow's Game theory for Political Scientists.
In addition, I recommend Osborne and Rubinstien. In addition we will cover
material from several journal articles. Below I list some additional text
that students might find useful.
Texts.
Morrow, James D. 1994 Game Theory for Political Scientists Princeton
NJ: Princeton University Press.
Osborne, Martin J. and Ariel Rubinstein 1994 A Course in Game Theory Cambridge MA: The MIT Press.
Fundenberg, Drew and Jean Tirole. 1991. Game Theory. Cambridge, MA: The MIT Press.
Myerson, Roger B., 1991. Game Theory: Analysis of Conflict. Cambridge MA: Harvard University Press.
Rasmusen, Eric. 1989. Games and Information Cambridge MA: Blackwell Publishers Inc.
Gibbons, Robert. 1992. Game Theory for Applied Economists Princeton NJ: Princeton University Press.
Banks, Jeffrey S. 1991 Signaling Games in Political Science. Chur Switzerland: Harwood Academic Publishers.
Course Outline.
Utility Theory
The properties of ordinal and cardinal preferences. Lotteries and expected
utility. Risk aversion and risk acceptance. Decision theory. (Readings:
Morrow Chpt. 1+2).
Introduction to Extensive Form and Normal Form Games:
Classic examples of normal form and extensive form games: prisoner's
dilemma, chicken, battle of the sexes, deterrence game, Cournot and Stackelberg
games.
Components of Games:
What are the components of a game? How are these components represented
mathematical? Integrating ideas into models: gameform, players, states,
action sets, strategy sets, payoffs, informational assumptions. (Readings:
Morrow Chpt. 3)
Nash Equilibria.
Nash equilibria in normal form games. Mixed strategy Nash equilibria.
The existence of Nash equilibria. (Readings: Morrow Chpt. 4)
Alternative Solution Concepts.
Iterative dominance-rationalizability, Minimax, Cooperative game theory:
Nash bargaining solution (Readings: Morrow Chpt. 4; Fudenberg and Tirole
Chpt. 2; Osborne and Rubinstein 53-64.)
Extensive Form Games.
Examples of common extensive form games. The credibility of Nash Equilibria
and an introduction to sub-game perfection. Backwards induction. "Trembling-hand"
perfect equilibrium. (Readings: Morrow Chpt. 5; Osborne and Rubinstein
Chpt. 6)
Correlated Equilibria.
(Readings: Osborne and Rubinstein p.44-48; Fudenberg and Tirole p.
53-59)
Legislative Voting Theory.
The median voter theorem. Sincere vs. sophisticated voting. Agenda
control and structure induced equilibria to overcome the chaos problem.
(Readings: Morrow p133-145.)
Bargaining theory.
Rubinstein's bargaining solution. Pork barrel model of legislatures.
Two-level games as models of international negotiations. (Readings: Morrow
p. 145- 156; Osborne and Rubinstein Chpt. 7)
Modeling Incomplete and Imperfect Information.
Introduction: Stochastic rather than deterministic outcomes. Private information modelled as type. Bayesian updating. (Readings: Morrow Chpt. 6; Fudenberg and Tirole p. 209-215)
Solution Concepts:
Bayesian equilibrium, perfect Bayesian equilibrium, and sequential
equilibrium. The Beer-Quiche game. Burning money and deterrence games.
(Readings: Morrow chpt.7, 8)
Principal-Agent problems
Incentive compatibility.
Out-of-equilibrium beliefs: defining beliefs that are unspecified by
Bayes Rule. (Readings: Banks p. 13-16; Morrow p.241-250).
Costly Signaling Games.
Information transmission in legislatures. (readings: Morrow p. 227-237;
Banks Chpt. 3).
Cheap Talk Signalling Games.
The threat of Presidential veto in bargaining. (Readings: Banks p.
50-53)
Timing games.
For example, wars of attrition (Readings: Fudenberg and Tirole p.117-126,
216-219)
Repeated Games
(Readings: Morrow Chpt. 9; Fudenberg and Tirole Chpt. 5+ 9; Osborne
and Rubinstein Chpt. 8)
Finitely repeated games: 3 period chicken. The chain store paradox.
Infinitely Repeated Games and the Folk Theorem. The possibility of
cooperation in the prisoner's dilemma through the formation of institutions.
Problem sets will be pasted here in postscript and pdf.