Thesis Defense: Exploration of the Three-Player Partizan Game of Rhombination

Posted on: April 10, 2017

Exploration of the Three-Player Partizan Game of Rhombination

Katie Greene

April 11th at 11:00 am in Manchester 020

We introduce a new combinatorial three-player partizan game called Rhombination and expand some ideas from two-player game theory into three-player game theory.

Three-dimensional Domineering, as defined by Cincotti, is distinct from Rhombination. We prove the Fundamental Theorem for three-player games, given the player preference set by Li. We set a bound on the number of games born on day n. Comparisons are made with Cincotti’s partial ordering and a generalization of two-player partial order is defined for three-player games. We make observations on outcome classes of games and find effects of rotation and reflection on outcome. We give many ideas for future theorems to prove or directions to take, including a potential method for defining three-player number games.