An Optimal Control Problem Arising from an Evolutionary Game

Open Access
Author:
Cai, Wente B
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Chris Griffin, Thesis Supervisor
  • Nate Brown, Honors Advisor
Keywords:
  • game theory
  • evolutionary game theory
  • optimal control
Abstract:
This paper is an integrative study of evolutionary game theory and optimal control. We first study the basics of evolutionary game theory and introduce the model that we would like to study based on the game of Rock-Paper-Scissors. We then move on to an introduction of optimal control and identify the requirements that need to be fulfilled in order for a solution to become optimal. Finally, we explore different methods of modeling the Rock-Paper-Scissors game as an optimal control problem and try to find an optimal control that minimizes the cost of the game. Various linearization schemes are attempted and the results are discussed.