1.
Game
Theory and Evolutionary Biology: Game theory is used by
biologists to model the interactions between individuals competing for
resources (food, mates, territory, etc.) and to offer an explanation for
the evolution of cooperative and competitive strategies. A good
place to start exploring the subject is the website of Holy Cross
Biology Professor Ken Prestwich:
http://www.holycross.edu/departments/biology/kprestwi/behavior/ESS/ESS_index_frmset.html
The pioneer of this field was the biologist John Maynard Smith; you may
want to take a look at his book
Evolution
and The Theory of Games, which is quite readable, for a classic.
2.
Combinatorial games and Surreal Numbers: The
incredibly creative mathematician John H. Conway used combinatorial
games as a vehicle for exploring the real number system, and beyond.
His ideas were presented in the books
Winning Ways for your Mathematical Ways
and
On Numbers and Games. The
name "surreal numbers" for Conway's creation was coined by computer
scientist Donald Knuth, and was the title of a novel (!) by Knuth
introducing Conway's ideas. On the web look at
http://www.usna.navy.mil/MathDept/wdj/surreal_numbers.html
or
http://en.wikipedia.org/wiki/Surreal_numbers
3. Game
Theory and Economics - Auctions: One of the most successful and
widely used applications of game theory is in the practice of auctions,
such as government bond auctions. Some of the basic ideas were developed
by John Nash (of
A Beautiful Mind
fame). For an introduction, see
http://courses.temple.edu/economics/Game%20Outline/index02.htm
4. Game
Theory and Political Science - Voting Theory: The controversies
surrounding the 2000 presidential election campaign brought into
question not only the particulars of how we cast votes (via voting
machines, paper ballots, etc.) but also the mechansisms for selecting a
winner (majority, plurality, electoral college, etc.) Game theory has
been appled to the study of voting. See
http://en.wikipedia.org/wiki/Voting_theory
5.
Gambit: This is a fairly sophisticated free software
package for investigating games, available at
http://econweb.tamu.edu/gambit/
The goal of this project is to become familiar with the software, and
explain its use.