Three Essays on Game Theory and Computation

Abstract

The results section of my thesis includes three chapters. The first two chapters are on theoretical game theory. In both chapters, by mathematical modelling and game theoretical tools, I am predicting the behaviour of the players in some real world issues. Hoteling-Downs model plays an important role in the modern political interpretations. The first chapter of this study investigates an extension of Hoteling-Downs model to have multi-dimensional strategy space and asymmetric candidates. Chapter 3 looks into the inspection game where the inspections are not the same in the series of sequential inspections. By modelling the game as a series of recursive zero-sum games I find the optimal strategy of the players in the equilibrium. The forth chapter investigates direct optimization methods for large scale problems. Using Matlab implementations of Genetic and Nelder-Mead algorithms, I compare the efficiency and accuracy of the most famous direct optimization methods for unconstraint optimization problems based on differing number of variables.