Introduction to Multi-schema Game Theory

Open Access
Author:
Suhey, Paul Robert
Area of Honors:
Chemical Engineering
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Darrell Velegol, Thesis Supervisor
  • Darrell Velegol, Honors Advisor
  • Andrew Zydney, Faculty Reader
Keywords:
  • game theory
  • schema
  • enzyme kinetics
  • Nash Equilibrium
  • thermodynamics
Abstract:
The primary purpose of this work is to introduce “schemas” into game theory to produce a new way in which to view Nash Equilibrium. Functioning similarly to enzymes in a chemical reaction, schemas eliminate the need to incorporate motivations into player utility functions, lessen subjective analysis, and allow games to be viewed via an engineering “systems” perspective. After mathematically defining several schemas (i.e. selfish, global, and fair), two solvers were created to predict the equilibrium outcome of real-world problems simplified into 2x2 player games. As predicted, games with new schemas produced different optimal strategies for players in even the most well-known games. Furthermore, a player’s schema distribution was predicted from experimental results found in literature. The concepts described herein could lead to the development of a new, more robust game theory model.