Game theory in incomplete information

Abstract: This thesis is about game theory, its general application to different games, and its different notions. We are going to focus on how different solutions can be found depending on how we view the game in question. We will particularly focus on games where the information is incomplete. In order to do so, we will use a game named ”The battle of sexes” as a guide throughout the entire thesis. We will adapt that game to the different kinds of games we will talk about. The importance with game theory and why it is an interesting field of study is that it gives a way to mathematically understand and analyse various situations in different other fields and real life areas. In this thesis we will not go deeper into the applications of game theory, but will mostly focus on the mathematical part of the field, and understanding how to find different desired outcomes for a given game. We will primarily lay out the fundamentals of game theory, in order for the reader to understand the basic notions of a game, a equilibria, and have the necessary knowledge to explore the field. Guillermo Owen’s book Game theory covers the field in a wider sense than this thesis, and is an interesting lecture to broaden ones knowledge on game theory.