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My Mini Course in Epistemic Game Theory |
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Introduction I have developed a mini-course in epistemic game theory. The purpose of this course is to introduce Master students, PhD students and researchers to the world of epistemic game theory. Epistemic game theory is not a specialization within game theory, but rather a particular way to look at game theory. The purpose of epistemic game theory is namely to model, and analyze, possible ways in which a player in a game may reason about his opponents. This reasoning process is really fundamental in game theory: before a player makes a choice in a game, he must form a belief about what his opponents will do, which in turn is based on what he believes that his opponents believe that others will do. That is, before making a choice, a player must reason about his opponents, and subsequently base his choice on this process of reasoning. My approach in this course In this course, I use the following four-step approach: 1. We first identify an intuitive way of reasoning about your opponents, by means of one or several examples. 2. In order to fully understand the behavioral consequences of this way of reasoning about your opponents, it is necessary to build a formal mathematic model that precisely describes the way of reasoning. 3. Once such a model has been delivered, we can logically derive the choices that a player can rationally make if he follows this pattern of reasoning. 4. If possible, we present an algorithm that computes, for a given player, all the choices he can rationally make if he follows this pattern of reasoning. About the course The course consists of six lectures. Each lecture will take approximately two hours. To every lecture there is a set of exercises that students and researchers can work on. Until now given, I have given the course at the following places:
Contents of the course 1.1. What is
game theory about? Part I : Standard beliefs in static games Lecture 1: Common belief in rationality Chapter 2: Common belief in rationality 2.1. Example:
Where to locate my pub Lecture 2: Epistemic foundation for Nash equilibrium Chapter 3: Epistemic foundation for Nash equilibrium 3.1. Definition of Nash
equilibrium Part II : Lexicographic beliefs in static games Lecture 3: Common weak belief in rationality Chapter 4: Common weak belief in rationality 4.1. Example: Should I call her
or not? Lecture 4: Proper rationalizability & An epistemic foundation for iterated weak dominance Chapter 5: Proper rationalizability 5.1. Example: To
which pub shall I go? Chapter 6: An epistemic foundation for iterated weak dominance 6.1. Iterated
weak dominance Part III : Conditional beliefs in dynamic games Lecture 5: Common initial belief in rationality Chapter 7: Common initial belief in rationality 7.1. Example: Father and son Lecture 6: Common strong belief in rationality & Epistemic foundations for backward induction Chapter 8: Common strong belief in rationality 8.1. Example: Father and son Chapter 9: Epistemic foundations for backward induction 9.1. Example:
Kramer versus Kramer
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