## Department of Mathematics

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Math 491: Game Theory

#### Course Objectives

Game Theory is a branch of applied mathematics that deals with problems of conflict and cooperation by postulating rational decision makers. It is used as a formal modeling tool in the Social Sciences and in Biology. It has been applied to issues such as nuclear deterrence, arms and trade rivalries, economic competition and collusion, legislative bargaining, and biological evolution. This course will introduce the students to the concepts and techniques of game theory and will develop their ability to understand, design, solve, and criticize game models. Class will be a mix of lectures, discussions, simulations, and laboratory using the GamePlan computer software.

#### Course Outline

Each topic below corresponds to about one week of classes, for a total of twelve weeks. The remaining three weeks will be devoted to the presentation and discussion of modeling cases.

I. Basic Game Theory
1: Normal and extensive form games, strategy, best reply, and equilibrium.
2: Introduction to the GamePlan software.
3: The fundamental theorem (John Nash).

4: Equilibrium path, beliefs, information, sequential rationality.
5: Games of incomplete information.
6: Repeated and dynamic games.

III. Basic Applications
7: Learning, signaling and screening.
8: Deterrence.
9: Social Dilemma.

10: Repeated continuous games.
11: Strategic Bargaining.
12: Games of timing.

#### Evaluation of Students

Students must complete two modeling tests, homework assignments, and a term project during the course of the semester. Grading is based on two modeling tests (20% each), homework and participation (20%) and the term project (40%). The term project can involve:

1. The modeling, testing, solving and critical discussion of a real-world problem that can be formulated in game theoretic terms; or
2. A term paper discussing the relations between Game Theory and your field of interest, or a topic relevant to the course material.

The term project can be an individual or a team (of no more than three individuals) effort. A team effort will be expected to be presented in class at the end of the semester. The term project must be defined and agreed on by the end of week 5.

#### Textbooks & Software

Submitted by: Jean-Pierre Langlois
Date: October 19, 2016