Noncoperative game theory : general overview and its application to the study of cooperation

Abstract

A game, in Game Theory, is a tool that can model any situation in which there are people that interact (taking decisions, making moves, etc) in order to attain a certain goal. This mathematical description of conflicts began in the twentieth century thanks to the work of John Von Neumann, Oskar Morgenstern and John Nash and one of its first motivations was to help military officers design optimal war strategies. Nowadays, however, Game Theory is applied to a wide range of disciplines, like Biology or Political Science, but above all, to Economy. Interestingly, eleven game-theorists have won the Economics Nobel Prize up to date but never has a Fields Medal been awarded to an expert in this field. This shows to what great extent Game Theory is important for Economy and at the same time how mathematicians regard it as a secondary discipline compared to other areas of Mathematics. This undergraduate thesis clearly falls under the category of applied mathematics or mathematical modeling and therefore its goal is far from just accurately proving a series of theorems. Instead, even if the foundations of Game Theory will be laid, I will focus on showing how Game Theory can be applied to solve a great number of different problems, like, for example, the emergence of cooperative dispositions towards strangers. Bearing this in mind, I will begin this undergraduate thesis by analyzing a military conflict between two countries whose officials will have a symbolic name: Nash and Neumann. To so do, I warn the reader that I will informally explain and use certain results that will be accurately justified later in this thesis.