Game Theory
Bard College

The final project for this course involves giving a talk on a topic related to Game Theory. You can work in groups of 2 or 3 people, or you can work by yourself. Here is some basic information:

- The talk should be about 5 minutes + 5 minutes/person (for example, one person should give a 10 minute talk, and two people should give a 15 minute talk).
- The talk must use computer slides (such as PowerPoint or Beamer).

Your talk should focus on explaining the main ideas of your topic clearly, so that the audience (the other members of the class) can understand it. For some of the topics listed below, there is too much material to present in the given time — in that case, you should choose some part of the material to present.

**Deadlines:**

**May 3:**Tell me which topic you are doing, and who is in your group. (Each group needs to choose a different topic, so that all of the presentations are different.)**May 10, 15, and 18:**Presentations occur.

Here are some possible topics. If you have ideas for other topics, come talk to me. When you decide on a topic, let me know as soon as possible (each group needs to have a different topic, and I'll cross out topics as I learn who is doing which topic). Your topic needs to be a topic that you don't already know, so make sure to choose a topic that you haven't seen in a different class.

**Topics from Textbook:**Here are some potential topics from the textbook:**Games with Incomplete Information**(Chapter 10)**Second-price auctions**(Section 4.6): This is a section in Chapter 4 that we skipped over. A 2 or 3 person group, should also look at Chapter 12, which is on Auction Theory, or at some other reference for Auction Theory.**Social Choice**(Chapter 21): This is about Voting Theory. You may want to look at another Voting Theory reference also, such as*Chaotic Elections!*by Donald Saari, which is in the Bard library.- Stable matchings (Chapter 22)

**Combinatorial Games:**We covered some combinatorial games (like Nim and Hex) at the beginning of the semester. Here are some possible topics on combinatorial games:- Nimbers: See me for the book
*Winning Ways for Your Mathematical Plays*by Berlekamp, Conway, and Guy. ~~Shannon Switching Game: See me for the book~~*Introductory Combinatorics*by Brualdi (the Shannon Switching Game is in Section 11.6).~~The Game of Sprouts: See Graph Theory and the Game of Sprouts by Mark Cooper.~~

- Nimbers: See me for the book
**Other Topics:****Modeling the Cuban Missile Crisis**: I recommend looking at Chapter 14 of the book*Games of Strategy*by Dixit and Skeath (I believe this book is in the library, but I also have a copy that you can borrow).- Simplex Algorithm and Linear Programming: See Sections 8.1–8.3 of
*Linear Algebra and its Applications*by Strang. The simplex algorithm is an algorithm for solving a linear programming problem. - Prisoner's Dilemma and Professional Sports Drafts
- Early Round Bluffing in Poker