Meetings: MW 3:30-4:50 p.m., Dougherty Hall 2315
Instructors: Peter Vanderschraaf, Baker Hall 161C, 8-8946,
peterv@andrew.cmu.edu, Office Hours:
Tuesday 2-4 p.m and by appointment
Grant Reaber, Baker Hall A60B, 8-8566, greaber@andrew.cmu.edu
Jiji Zhang, Baker Hall 138, 8-9669, jiji@andrew.cmu.edu
Prerequisites: Students need to be familiar with the material covered in the standard calculus sequence. In particular, students need to have some experience with solving systems of equations, ordinary and partial differentiation, and analyzing numerical sequences and series. Familiarity with the material covered in 80-305/88-356, Rational Choice, will prove helpful but is not a formal prerequisite. Students will be required to study the proofs of certain theorems and occasionally prove theorems for homework and exams, so a certain degree of “philosophical maturity” and “mathematical maturity” will be valuable in approaching this material.
Required Texts: Cristina Bicchieri, Rationality and Coordination (Cambridge), Martin Osborne, An Introduction to Game Theory (Oxford)
Course Description: Game theory is the branch of decision theory in which decision problems interact. This course will cover those parts of game theory of special interest to social scientists and philosophers. We will discuss specific elements of the formal theory, including: the distinction between cooperative and noncooperative games, games in the strategic and the extensive form, solution concepts, epistemic conditions needed to predict outcomes of games, equilibrium refinements, dynamical models of equilibrium selection, and folk theorems of indefinitely repeated games. We will discuss results in experimental economics that test some of the assumptions of classical game theory. Throughout the course we will examine applications of the formal concepts of game theory to problems in moral and political philosophy and the social sciences.
Schedule
Jan. 18 Organization meeting. First motivating examples.
Jan. 23 Historical development of game theory. Assumptions adopted by game theorists.
Jan. 25 Introduction to games in strategic form.
Jan. 30 The Nash equilibrium concept.
Feb. 1 Identifying equilibria in strategic form games.
Feb. 6 Epistemic foundations of the Nash equilibrium concept.
Feb. 8 Experimental tests of the Nash equilibrium concept.
Feb. 13 Games in the extensive form of perfect information.
Feb. 15 Games in the extensive form of imperfect information.
Feb. 20 The relationship between games in the strategic and the extensive form.
Feb. 22 Equilibrium refinements and backwards induction. Experiments findings of games in the extensive form.
Feb. 27 Applications of strategic and extensive form games in philosophy and the social sciences.
Mar. 1 Midterm 1.
Mar. 6 Rationalizability and correlated equilibrium.
Mar. 8 Epistemic foundations of solution concepts.
Mar. 20 Games of incomplete information. The Harsanyi transformation. Bayesian equilibria.
Mar. 22 Games of incomplete information (cont.).
Mar. 27 Applications of games of incomplete information in philosophy and the social sciences.
Mar. 29 Evolutionary models of equilibrium selection.
Apr. 3 Belief updating models of equilibrium selection.
Apr. 5 Generalizations of learning processes for correlated equilibria.
Apr. 10 Experimental tests of the validity of the dynamical models.
Apr. 12 Finite and indefinitely repeated Prisoners' Dilemma.
Apr. 17 Indefinitely repeated games with fixed counterparts.
Apr. 19 Indefinitely repeated games with variable counterparts.
Apr. 24 Evolutionary analyses of cooperation in repeated Prisoners' Dilemma.
Apr. 26 Midterm 2.
May. 1 The bargaining problem and the Nash program. Axiomatic solutions to the bargaining problem.
May. 3 Dynamic analyses of the bargaining problem.
TBA Presentation Meeting, Take-home Final Due