Jacob Peterson: Klimatkris, fredagsdejter och kannibalism: En introduktion till spelteori

Abstract: Game theory studies strategic situations in which the decisions of multiple agents affect each other’s outcomes. The subject is of great importance in fields such as mathematics, economics, and the social sciences. The aim of this thesis is to provide an introductory yet mathematically rigorous presentation of central aspects of finite game theory, with a focus on concepts, models, and results that are relevant for upper secondary education or further studies.
The thesis examines static games in normal form, where concepts such as pure and mixed strategies, dominance, best response, Pareto optimality, and Nash equilibrium are introduced. It also studies games in extensive form, where sequential decisions are modeled using game trees and analyzed through subgame perfect Nash equilibrium and backward induction. Games with imperfect information are further explored through information sets and the distinction between mixed and behavioral strategies.
A central component of the thesis is the existence of Nash equilibrium in finite games. This is presented through an analytical proof based on Brouwer’s fixed-point theorem and Sperner’s lemma. The thesis is intended to function both as an introduction to game theory and as an illustration of how mathematical models can be used to analyze conflict, cooperation, and rational decision-making.