PRISONER’S DILEMMA GAMES ON A GEODESIC DOME: A STUDY OF LOCAL INTERACTION IN OVERLAPPING, TWO-DIMENSIONAL NEIGHBORHOODS

Open Access
Author:
Wolf, William Abraham
Area of Honors:
Interdisciplinary in Industrial Engineering and Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Eli Christopher C Byrne, Thesis Supervisor
  • Paul Griffin, Honors Advisor
  • Leonid N Vaserstein, Honors Advisor
Keywords:
  • game theory
  • prisoners dilemma
  • local interaction
  • overlapping neighborhoods
Abstract:
The primary purpose of this work is to perform an exhaustive analysis of an N-player Prisoner’s Dilemma game, and study the effects of relevant parameter inputs on system dynamics. The model used was based upon that examined in two papers, Altruists, Egoists and Hooligans in a Local Interaction Model, and Cooperation, Mimesis, and Local Interaction, which are purposed similarly. However, three significant changes to this model were made: an updated learning rule, local and global beta-probabilistic player updates, and a geodesic world geometry. Of the combined five findings of the papers above, including total convergence to altruism, total convergence to egoism, perpetually “blinking” egoists, a steady pair of egoists, and a combination of both steady and “blinking” egoists, the former two were reproduced absolutely, and the latter three reproduced approximately. In addition, we provide strong conjecture for the gauranteed convergence of “blinking” cases given global updates, and substantial evidence for the symmetric support of local egoism that initially sustains this “blinking,” as well as that in similar cases. Furthemore, we observe and dissect “quasi-stable” systems, a trend of linear progression towards egoism given fixed neighborhood size n and increasing cost C, and a trend of lateral shift towards “quasi-stability” given fixed C and increasing n. Finally, we use our findings to make general commentary about real-world players, the dynamics of their interaction, and Prisoner’s Dilemma models themselves.