Mathematical Analysis of Games

Mathematical Analysis of Games
Project WISE, Spring, 1998
Center for High Pressure Research

This workshop, which is being conducted by the Center for High Pressure Research (CHiPR) for the Women in Science and Engineering (WISE) program at SUNY Stony Brook, will focus on games of strategy designed for one, two, and several players. These will include the Iterated Prisoner's Dilemma, Big Net Little Net, Lines, Undercut, Nim, Saltines, Sprouts, Fractal Fantasy, Othello, and Tower of Hanoi. Algorithms for winning and optimal strategies will be explored, and will be described using recursion, optimizing functions, and other methods. The applicability of the Prisoner's Dilemma and related games to real-life sociopolitical phenomena will be considered.

For our research this summer with Women In Science and Engineering at Stony Brook University, we participated in the Mathematical Analysis of Games. Our faculty advisors included Glenn and Janet. The workshop focused on games of strategy designed for one, two and several players. The games included the Prisioner's Dilemma, Big Net Little Net, Undercut, Saltines, Sprouts, and the Tower of Hanoi. After playing each game, we analyzed it. This included discussing possible strategies, different methods, and possible social implications to life. For some of the games we developed mathematical expressions to reason the components that make up each game. For example, in Sprouts we developed the expression 3n-1 to show the highest number of moves possible.
After each W.I.S.E. session, we took all of the necessary materials home to play some of the games. Then, we played the games with many people. We tried different methods and strategies, and wrote down the results. Then, in our next W.I.S.E. session we discussed the results, and their reasons. We talked about why what happened actually happenned, and how it could have been different. Overall, our project was a succcess.

Schedule
Session	Date	Activities
1	February 4, 1998	Overview Prisoner's Dilemma Big Net, Little Net Wolf's Dilemma Diamond Thief Applet on Project Java Lines Applet on Project Java Homework: Play Big Net, Little Net
2	March 3, 1998	Discuss Big Net, Little Net Societal Implications of Prisoner's Dilemmma Undercut Saltines Sprouts Blinder's Payoff Matrix and Nash Equilibrium Homework: Play Undercut
3	April 2, 1998	Discuss Undercut Nim Nimby Tower of Hanoi Recursion Homework: Play Nim and Nimby
4	May 6, 1998	Fractal Fantasy Wrap-up Prepare World Wide Web Reports