Game Theory: Some Course Information (2016)

Prepared by:

Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York

email:

malkevitch@york.cuny.edu

web page:

http://york.cuny.edu/~malk

The best way to reach me between classes is via email:

malkevitch@york.cuny.edu

My TC email address is:

jm3099@columbia.edu

but there is the risk that there will a delay in my seeing what you send there.

The optional text for this course will be:

Gura, Ein-Ya and Michael Maschler, Insights into Game Theory, Cambridge U. Press, 2008.

The assignments I will be giving are not taken from this book but for those who like to have a book to rely on, this book treats many (but not all) of the topics I will be covering. This is an interesting book because it served as the dissertation for Ein-Ya Gura for her doctorate degree in Mathematics Education at Hebrew University in Jerusalem.

I often send out emails between classes with information related to the course and to try to set the stage for the next class. You should look your Teachers College email account regularly.

You should also regularly consult the web page below which will serve as the "class web page."

http://www.york.cuny.edu/~malk/gametheory/index.html

The materials that are being put up for this semester are at the start but materials from prior versions of this course I have taught are probably worth a look. There is a lot of material related to game theory and fairness models on my web page but it is rather scattered around. You may enjoy seeing if there is any material that interests you.

http://www.york.cuny.edu/~malk/

In particular, look at my tidbits and bibliography pages.

Other materials I have written related to games and fairness appear in the Feature Column of the American Mathematical Society whose archive is here:

http://www.ams.org/samplings/feature-column/fcbrowse?category=Game%20Theory%20and%20Social%20Choice


The goal of the Feature Column is to improve public perceptions of mathematics and to show a general audience the breadth of mathematics.

There are many blogs which deal with game theory/economics/fairness. Two noteworthy ones are:

Alvin Roth - Market design. (Roth shared the 2012 Nobel Memorial Prize in Economics with another game theorist - Lloyd Shapley.)

http://marketdesigner.blogspot.com/

Turing's Invisible Hand. (Algorithmic game theory and related topics, run by a group of individuals interested in games, computer science, and economics - not active recently.)

http://agtb.wordpress.com/

In addition to the game theory and fairness models I will teach in this class, I am also interested in geometry and many other kinds of mathematics. I particularly like the quick starting nature of game theory and geometry, their many applications, and the ease of stating unsolved problems in these areas as a way foster interest in mathematics by students in lower grades.

There will be a final on the last day of class. Doctoral students must complete a project but anyone who wants to do a project can do so. Details about the project will be forthcoming.

I will be be providing many handouts, most of which will also be available via the class web page above. You may want to get another class member to collect copies of handouts for days on which you are absent. Many of the handouts are "practice" problems for you to work on but those assignments which I expect to be handed in will be announced well in advance.

I hope you will ask lots of questions in class. Asking questions is the key to learning mathematics and in my view there is no such thing as a "silly" or "stupid" question. Questions also help me in understanding what aspects of the material presented may need more attention.

Recently, many US states adopted the Common Core State Standards in Mathematics (CCSS-M). While I am saddened by this development (I am not a fan of Standards in general and I think the original NCTM Standards were better, if not "common"), game theory is a very attractive way to implement the modeling component of the CCSS-M. I will try to show how game theory can be used in support of topics in the "traditional" mathematics K-12 curriculum even if the CCSS-M "forbid" it as an explicit part of what can be taught as important mathematics. In general I am a believer in breadth over depth and believe that curriculum should be "a mile wide and an inch deep."

Because there will be a US presidential election in November 2016, and there are currently party primaries that are going on, I will emphasize game theory topics that involve elections and voting in this course. Many of these topics can serve as the basis for classroom lessons for those of you who are teaching this semester.

I hope you enjoy the course!