# Intro to Game Theory:

Many important phenomena in economics and political science involve strategic interaction among small numbers of agents. Examples include competition between oil producing nations, bargaining over the price of a car, and forming voting coalitions in a legislature. Game theory is the mathematical tool that social scientists use to model these phenomena. This course will provide an introduction to the fundamental concepts of modern game theory and applications to the social sciences.

## Syllabus:

### Course Goals

This course is an introduction to game theory, the study of strategic behavior among parties having opposed, mixed or similar interests. This course will sharpen your understanding of strategic behavior in encounters with other individuals. You will learn how to recognize and model strategic situations, to predict when and how your actions will influence the decisions of others and to exploit strategic situations for your own benefit. The course aims to provide students with a basic understanding of the language and concepts of game theory, as well as providing some surveys of important theoretical models within the field.

### Course Outline:

#### Overview Class

#### Decision Theory and Math review:

- Utility representations of preferences
- Math review of functions and notation.
- Probability and Expectations
- von Neumann-Morgenstern representation
- Choice, and revealed preference
- Examples
- Sequences (reviewed as needed for new material)
- Calculus and Optimization (reviewed as needed for new material)

#### Game Theory basic building blocks

- Dominance
- Equilibrium: pure strategies
- Equilibrium: Mixed Strategies
- Basic games: Prisoner's dilemma, Matching Pennies, Battle of the Sexes, Stag Hunt, Dove-Hawk
- Continuous Games: Cournot and Bertrand; Public Goods

#### Extensive-Form Games

- Game trees
- Sub-game perfection
- Forgetful driver game
- Stackelberg and other Illustrations
- Refinements (maybe)

#### Repeated Games

- Finitely repeated games
- Infinitely repeated Games
- Folk theorems

#### Incomplete Information

- Bayesian games
- Auctions
- Signalling
- Voting
- Cheap Talk & Strategic Communication

#### Cooperative Game Theory & Social Choice

- Coalitions
- The core

#### Bargaining

- Rubinstein's model
- Nash bargaining

#### Extensions (If time allows)

- Rationalizability Evolutionary Game Theory

## Assessment:

- There will be two midterms and an optional final examination, as well as 5 homework assignments.
- The homeworks will count for 10% of your grade, and each homework will be assessed coarsely out of 2. However, exam questions will be similar to, and at the same level as homework questions, so doing the homeworks is fairly important.
- 2 means perfect.
- 1 means a decent effort was made, but not everything was correct.
- 0 if the homework was not turned in, or was very incomplete/incorrect.
- Solutions will be provided to allow you to see where you went wrong.
- Late homeworks are not accepted, and will receive a 0.

- If you choose not to take the final then the two midterms will count for 40% and 50% of your final grade.
- If you choose to take the optional final the midterms will count for 20% and 25% of your final grade, with the final counting for the remaining 45%.
- If you turn in the final examination it will count for 45% of your final grade.
- If you do not turn in the final examination only the two midterms will count at 40% and 50%, respectively.

- There are no make-up exams, and there is no extra credit for this course.

## Text Books:

- An Introduction to Game Theory, by Martin J. Osborne, Oxford University Press, 2004.
- Available from Pitt Bookstore, Amazon, etc.

- Additionally you might find the following useful for supplementary reading:
- Games of Strategy, 3rd Edition, by Avinash Dixit, Susan Skeath and David Reiley, W.W. Norton & Co, 2009. Hillman HB144.D59

- For more advanced texts at the graduate level, see the below texts in the library:
- A Course in Game Theory, by Martin J. Osbourne and Ariel Rubinstein, MIT Press, 1994. Hillman Library, HB144.O733 (see Martin Osbourne's site too)
- Game Theory, by Drew Fudenberg and Jean Tirole, MIT Press, 1991. Hillman Library, HB144.F83