Subcategory: Physics (not Nanoscience)
Ricky Dixon - Mississippi Valley State University
Co-Author(s): Neal Solmeyer and Radhakrishnan Balu, Army Research Laboratory, Washington, DC
Game theory is the study of the mathematics behind rational decision making; mainly used in economics, political science, and psychology. Quantum game theory takes game theory and introduces superposed initial states, quantum entanglement of initial states, and superposition of strategies used. We believe that quantized games could be of great use in both networking and cybersecurity. The purpose of this research is to expand this to games where players do not have complete information about the game, i.e. Bayesian games, and study the benefits of quantized games as opposed to classical games. This research began with studying classical two player games. The games used were the Prisoner’s Dilemma and DA Brother’s game. Using the Mathematica software, a code was created to run simulations of these games to find the Nash equilibria (NE). This was done to get a better understanding of the different player payoffs and how they related to the NE. Next these games were quantized. Using the program that was written, we were able to study the payoff and NE as a function of the entanglement. In order to obtain efficient curves in the data we ran the games with steps of pi/16 entanglement from 0-pi/2 with 0 being no entanglement and pi/2 being maximal entanglement. From the data it was seen that the Prisoner’s Dilemma game the NE disappeared at a relatively low amount of entanglement whereas with the DA Brother’s game there was still a NE at maximal entanglement. Once the analysis of these games were completed a Bayesian game was created where Player A was a general player, Player B1 was a Prisoner’s Dilemma type player, and Player B2 was a DA Brother’s type player. In the Bayesian game Player A has a possibility, P, of playing with player B1 and possibility (1-P) of playing with player B2. In this game entanglement held the same values as in the classical game and the value of P was in the range of 0-1 in steps of 0.1. In order to analyze this game three dimensional gaps were created in order to see the NE as a function of not only entanglement but also as a function of P. From these graphs it was observed that although the payoffs at the NE varied in response to P, the curves were similar to those seen in the initial two player games. In the future works we would like to study the NE to find any patterns and also find applications for quantized games.
Funder Acknowledgement(s): I wish to acknowledge the mentorship of both Neal Solmeyer and Radhakrishnan Balu and the sponsorship of the Thurgood Marshall College Fund and the Army Research Laboratory.
Faculty Advisor: Latonya Garner, firstname.lastname@example.org
Role: In this research I was responsible for running the simulations, creating all graphs necessary for analysis, analyzing the data, and modifying the program to make it more efficient.