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Über dieses Buch

This is a textbook for university juniors, seniors, and graduate students majoring in economics, applied mathematics, and related fields. Each chapter is structured so that a core concept of that chapter is presented with motivations, useful applications are given, and related advanced topics are discussed for future study. Many helpful exercises at various levels are provided at the end of each chapter. Therefore, this book is most suitable for readers who intend to study non-cooperative game theory rigorously for both theoretical studies and applications.

Game theory consists of non-cooperative games and cooperative games. This book covers only non-cooperative games, which are major tools used in current economics and related areas. Non-cooperative game theory aims to provide a mathematical prediction of strategic choices by decision makers (players) in situations of conflicting interest. Through the logical analyses of strategic choices, we obtain a better understanding of social (economic, business) problems and possible remedies. The book contains many well-known games such as the prisoner’s dilemma, chicken (hawk–dove) game, coordination game, centipede game, and Cournot, Bertrand, and Stackelberg models in oligopoly. It also covers some advanced frameworks such as repeated games with non-simultaneous moves, repeated games with overlapping generations, global games, and voluntarily separable repeated prisoner’s dilemma, so that readers familiar with basic game theory can expand their knowledge. The author’s own research is reflected in topics such as formulations of information and evolutionary stability, which makes this book unique.



Chapter 1. Games in Game Theory

This chapter explains what a “game” means in game theory and gives classifications of games. Rationality in game theory is also discussed.

Takako Fujiwara-Greve

Chapter 2. Strategic Dominance

This chapter formulates normal-form (strategic-form) games, explains strategic dominance, and introduces an equilibrium concept through iterative elimination of strictly dominated strategies.

Takako Fujiwara-Greve

Chapter 3. Nash Equilibrium

The fundamental equilibrium concept of non-cooperative game theory, Nash equilibrium, is explained by many examples and is formally defined. Relationships with the iterative elimination of strictly dominated strategies are proved and Existence Theorem is proved.

Takako Fujiwara-Greve

Chapter 4. Backward Induction

Extensive-form games are defined, and an equilibrium concept through backward induction is introduced for games with perfect information.

Takako Fujiwara-Greve

Chapter 5. Subgame Perfect Equilibrium

For general extensive-form games with or without perfect information, subgame perfect equilibrium is defined. Various repeated games are analyzed, and Perfect Folk Theorem is proved.

Takako Fujiwara-Greve

Chapter 6. Bayesian Nash Equilibrium

In this chapter, we explain Harsanyi’s Bayesian framework for games with incomplete information. For normal-form games with incomplete information, Bayesian games and Bayesian Nash equilibrium are defined.

Takako Fujiwara-Greve

Chapter 7. Perfect Bayesian Equilibrium

In this chapter we consider extensive-form games in which the payoff functions are not common knowledge. We introduce the concept of Perfect Bayesian Equilibrium and analyze signaling games.

Takako Fujiwara-Greve

Chapter 8. Equilibrium Refinements $$^{**}$$ ∗ ∗

It is often the case that a game has many Nash equilibria. In this chapter, we introduce equilibrium refinements based on stabilities under small perturbations. As a famous application of sequential equilibrium, we explain the chain store paradox with incomplete information.

Takako Fujiwara-Greve

Chapter 9. Equilibrium Selection $$^{*}$$ ∗

In this chapter, we introduce notions of payoff dominance and risk dominance, explain their meanings, and also extend the risk dominance concept to p-dominance. In addition, we illustrate how equilibrium selection is performed using the example of global games, which is relevant to many economic situations.

Takako Fujiwara-Greve

Chapter 10. Evolutionary Stability $$^*$$ ∗

It is possible to talk about the stability of a strategy distribution without relying on an individual player’s choice. This is evolutionary stability. In this chapter, we give some “static” stability notions based on the payoff comparison and one dynamic stability concept based on the replicator dynamic, which is most widely used.

Takako Fujiwara-Greve


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