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Activity Number: 253 - Contributed Poster Presentations: Section on Statistical Computing
Type: Contributed
Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract #329141
Title: A Computational, Data-Driven Approach to Game Theory
Author(s): Michael Alexander Smith* and Mark Daniel Ward and Deidra Coleman and Doug G Crabill and Jamylle Carter and Jennifer Travis and Jack Henry Good and Bret Benesh
Companies: Purdue University and Purdue University and Wofford College and Purdue University and Diablo College and Lone Star College and Purdue University and College of Saint Benedict and Saint John's University
Keywords: Game Theory; Data-Driven; Subtraction Games

In a two-player subtraction game, the players remove stones from a pile, until one player is stuck, so the other wins. Subtraction sets with one or two allowable move sizes have been understood since the 1970's, but a precise characterization of the game with three allowable move sizes x,y,z remains unknown. We used 37 years of computation, and more than 6 TB of data, in a massive data-driven approach to a full characterization of these periodicity. In the three-dimensional space that characterizes the game, we have recently developed a full characterization that holds, except for a neighborhood near the plane x+y=z. During the past six months, we uncovered the complex structure near the plane x+y=z as well. We will use a three-dimensional visualization to display the fractal nature of the underlying principles of this game. We next endeavor to introduce a methodology for pinpointing the structure of the game at any point (without traditional recursive brute-force computations), which will yield additional insights into the structure. This material is supported by NSF grant 1246818 and by the NSF-sponsored REUF program of the American Institute of Mathematics.

Authors who are presenting talks have a * after their name.

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