Abstract

This report will take you on a journey through the fascinating world of game theory, the mathematical study of how people or groups make decisions in situations where their actions affect each other. You will see how game theory can help us explain and predict various phenomena, such as why civilizations may hide in the dark forest of the universe, how nuclear weapons can prevent wars, how criminals can cooperate or betray each other, and how cooperation can emerge among selfish individuals. You will also take a glimpse of the basic concepts and tools of game theory, such as single person games, representation theory of weak orderings, fixed-point theorem, Nash equilibria, games on graphs, and the dynamics of cooperation. By the end of this report, you will have a better understanding of game theory, its central role in economic and social research, and its applications to various other fields and disciplines.