Introduction to Game Theory

This book has set itself the task of providing an overview of the field of game theory. The focus here is above all on imparting a fundamental understanding of the mechanisms and solution approaches of game theory to readers without prior knowledge in a short time. Because game theory is in the first place a mathematic discipline with very high formal demands, the book does not claim to be complete. Often, the solution concepts of game theory are mathematically very complex and impenetrable for outsiders. However, as long we remain on the surface, some principles can be explained plausibly with relatively simple means. For this reason the book is eminently suitable in particular as introductory reading, so that the interested reader can create a solid basis, which can then be intensified through advanced literature.

What are the advantages of reading this book? I believe that through the fundamental understanding of game theory concepts, the solution approaches that are introduced can enlighten in nearly all areas of life – after all, along with economics, it is not for nothing that game theory is applied in a huge number of disciplines, from sociology through politics and law to biology.

With this in mind I hope you have a lot of fun reading this book and thinking!

1. Foreword 
   
2. Introduction 
   
   1. Aim and task of game theory 
      
   2. Applications of game theory 
      
   3. An example: the prisoner’s dilemma
      
   4. Game theory terms 
      
3. Simultaneous games 
   
   1. Foundations 
      
   2. Strategies 
      
   3. Equilibriums in pure strategies 
      
   4. Equilibriums in mixed strategies 
      
   5. Special forms of games 
      
   6. Simultaneous games in economics 
      
   7. 3-person games 
      
4. Sequential games 
   
   1. Foundations 
      
   2. Terms 
      
   3. Subgames and subgame perfect equilibriums 
      
   4. Sequential games played simultaneously and Nash equilibriums
      
   5. The First Mover’s Advantage (FMA) 
      
   6. An example: the Cuba crisis 
      
5. Negotiations (cooperative games)
   
   1. Foundations 
      
   2. Coalitions 
      
   3. The characteristic function 
      
   4. The cake game 
      
   5. Negotiations between two players 
      
   6. Distinguishing cooperative and non-cooperative games 
      
6. Decisions under uncertainty 
   
   1. Modelling uncertainty 
      
   2. The utility function u(x) 
      
   3. The expected utility 
      
   4. The St. Petersburg Paradox 
      
7. Anomalies in game theory 
   
   1. Foundations 
      
   2. Games under uncertainty: the Ellsberg paradox 
      
   3. Games without uncertainty 
      
8. References 
   
9. List of abbreviations 
   
10. Biography