A Computational, Data-Driven Approach to Game Theory

• 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
• 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

Abstract

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.