Nathan Wolfe is a rising sophomore from Winchester, Massachusetts, attending the Roxbury Latin School. He has been interested in both mathematics and robotics since a very young age. He is now finding success in math competitions, including qualifying for the USAJMO, and he also captains his school's robotics team and plays first trumpet in the Roxbury Latin jazz band. In his spare time he enjoys playing tennis and soccer.
Project: The Subtraction Game
With two players, the subtraction game (a variant of Nim) is easily solvable. However, with three players, teamwork becomes essential to win. At certain points in a game, one player influences the chances of the others winning, without a direct consequence to him or herself for choosing either move. The simulated players in this Demonstration use a tit-for-tat strategy, punishing in exchange for punishment and rewarding in exchange for reward. The sliders change how many favors the player will perform in exchange for one favor from another. Results from each match are graphed.