Syllabus Thinking Strategically (EBC2082) 2022/2023 Organization of the course The course is based on the book "Epistemic Game Theory: Reasoning and Choice" by Andrés Perea. More information about the book can be found under "Resources" at the opening page. Every week will start with a theory lecture on Monday in which typically a chapter of the book (or parts of it) will be discussed. Exceptions are Weeks 4 and 7, which focus on economic applications which are not taken from the book. You are advised to study this chapter before attending the lecture. During this lecture, you can ask questions. After studying the theory and following the lecture, you can do a practice quiz which consists of ten conceptual questions about the theory of that week. This quiz will help you verify whether you have understood the relevant theoretical concepts for that week. For those questions you struggled with, it is advised to review that part of the theory again. Your quiz score does not count for the final grade. The quiz is only there to help you. After you have done the practice quiz, it is time to do the exercises for that week. Typically, the exercises will be problems from the book, except for Weeks 4 and 7. For those weeks you can find the exercises directly in the module of that week. These exercises will be of a different nature than the quiz questions, as they will train you to apply the theory to practical problems. Each problem is based on a story. The first step will always be to translate the story into a game. Then, you will be asked to apply the concepts of that week, and possibly of earlier weeks, to analyze that game. Please make pictures of your solutions to the exercises, as you will need them for the tutorial meetings. If you wish, you can also prepare the exercises on the computer, but that's you own choice. Every week there will also be a tutorial meeting on Wednesday. At the beginning of the meeting we will verbally discuss the quiz questions of that week, after which we will turn to discussing the exercises you prepared. All discussions will take place in an interactive fashion: For each of the quiz questions, the tutor will ask a student to explain his or her answer to the fellow students. For each of the exercises, the tutor will ask a student to present his or her solution to (a part of) the problem, based on his or her (pictures of the) solutions. Please have these solutions ready on your laptop, so that you can share your screen when you are asked to. Your performance during the tutorial meetings will be graded, and this will determine your participation grade. Exam and grading At the end of the course, there will be a written exam. No books or notes are allowed during the exam. Your exam score will be a grade between 0 and 10. As mentioned earlier, you will also receive a participation grade, based on your performance during the tutorial meetings. Good performance does not necessarily mean that you always present a perfect solution to the quiz questions and exercises. It rather means that you come to class well- prepared, that you study the literature and seriously prepare the quiz questions and exercises before the tutorial meeting, and that you actively and constructively participate during these meetings. Also your participation score will be a grade between 0 and 10. For every tutorial meeting you miss, your participation grade will be lowered by 1. If you miss more than two meetings, your participation grade will be insufficient (lower than 5.5). Your final grade will be based for 70% on the exam grade and for 30% on the participation grade. To pass the course, both your exam grade and participation grade must be at least 5.5. If you have an insufficient exam grade but a sufficient participation grade, you must do the re-sit exam. The participation grade will remain valid. If you have a sufficient exam grade but an insufficient participation grade, you must do a course assignment to pass. If both your exam grade and your participation grade are insufficient, you must do a course assignment and the re-sit exam. Topics week by week Week 1: Belief in the opponent’s rationality Read: Chapter 2, Sections 2.1 - 2.8. Exercises: Chapter 2 Problem 2.1, except part (d) Problem 2.2, except part (e) Problem 2.4, except parts (d) and (f) Hint to Problem 2.4 (b): Show first that blue and brown are not strictly dominated by another (nonrandomized) choice. Show next that blue and brown are not strictly dominated by a randomization over two choices. Show finally that blue and brown are strictly dominated by the randomized choice where you choose red with probability 0.17, green with probability 0.21, black with probability 0.26, and white with probability 0.36. You will learn the following: • • • • • • • • • • What is a game What is a utility function What is a belief about the opponents' choices How can these beliefs be visualized by a beliefs diagram What is expected utility What does it mean to choose rationally given your belief What is a strictly dominated choice, and its relation to choosing rationally What does it mean to believe in the opponent's rationality How to use the beliefs diagram to determine which choices you can rationally make if you believe in the opponents' rationality (graphical method) How to use a recursive procedure (algorithm) to determine which choices you can rationally make if you believe in the opponents' rationality Week 2: Common belief in rationality Read: Chapter 3, Sections 3.1-3.5, and 3.7. Exercises: Chapter 3 Problem 3.1, except part (d) Problem 3.2, except part (d) Problem 3.4, except parts (d) and (g) You will learn the following: • • • • • • • • • • • What are beliefs about the opponent's beliefs What is a belief hierarchy How can a belief hierarchy be visualized by a beliefs diagram How can you derive a belief hierarchy from a beliefs diagram How can a belief hierarchy be encoded by an epistemic model with types How can you derive a belief hierarchy from an epistemic model What does common belief in rationality mean intuitively How can common belief in rationality be formalized within an epistemic model How can common belief in rationality be checked within a beliefs diagram Use a beliefs diagram to find those choices you can rationally make under common belief in rationality (graphical method) Use a recursive procedure to find those choices you can rationally make under common belief in rationality (algorithm) Week 3: Simple belief hierarchies and Nash equilibrium Read; Chapter 4, Sections 4.1, 4.2 and 4.3 Exercises: Chapter 4 Problem 4.1 Problem 4.2 Problem 4.7, except part (b) Hint for Problem 4.2 (d): This part is difficult. Conclude first that in a Nash equilibrium, your choice 2 and Barbara's choice 2 must receive probability zero. Next, try to show that (ace, ace) is the only Nash equilibrium. For this, use the following steps: Show that your choice 3 must receive probability zero in a Nash equilibrium. To show this, suppose that your choice 3 would receive positive probability in a Nash equilibrium. Then, your choice 3 must be optimal in the Nash equilibrium. Show that this is only possible if Barbara's choice 3 receives positive probability, and hence Barbara's choice 3 must be optimal in the Nash equilibrium. Next, show that this is only possible if your choice 4 receives positive probability, and hence your choice 4 must be optimal. Hence, both your choices 3 and 4 must be optimal in the same Nash equilibrium. In particular, your choices 3 and 4 must give the same expected utility. Conclude from this that the probability assigned to Barbara's choice 3 must be 15/13 times the probability assigned to Barbara's choice 4. Show that this implies that your expected utility from choosing 3 is negative, and hence 3 cannot be optimal for you. But then, your choice 3 should not get a positive probability in a Nash equilibrium. In a similar way, try to show that your choice 4 should also not receive positive probability in a Nash equilibrium. Hence, the only choice for you that can receive positive probability in a Nash equilibrium is ace. Hint to Problem 4.7 (c): Also this part is difficult. Consider person 1. Show first that it can only be optimal to go for person 1 in a Nash equilibrium if the Nash equilibrium assigns probability at least 2/3 to person 2 going. Show that in this case, person 3 would not go. Conclude from this that person 2 would then also not go. Conclude from this that person 1 should not go either. Hence, in a Nash equilibrium it cannot be optimal for person 1 to go. Explain why the same holds for all other persons as well. You will learn the following: • • • • • • • • • What is a simple belief hierarchy How to combine common belief in rationality with the requirement of a simple belief hierarchy What is a Nash equilibrium Understand that common belief in rationality in combination with a simple belief hierarchy leads to Nash equilibrium Why Nash equilibrium is stronger than just common belief in rationality How to compute Nash equilibria in a game How to use Nash equilibrium to find those choices you can rationally make under common belief in rationality with a simple belief hierarchy Analyze examples where Nash equilibrium is more restrictive than common belief in rationality Realize that Nash equilibrium may impose unnatural restrictions Week 4: Economic applications of static games Exercises: Problems 1, 2, 3 and 4 from problem set week 4. In the lecture we will apply the concepts of common belief in rationality and Nash equilibrium to some economic models. In particular, we will look at: • • price competition between firms that offer differentiated goods competing firms that must choose their product characteristic You will learn the following: • • • How to translate certain economic models into games How to analyze such economic models by using common belief in rationality and Nash equilibrium Understand the strategic thinking of economic actors Week 5: Belief in the opponent’s future rationality Read: Chapter 8, Sections 8.1 - 8.6, and 8.8 - 8.11 Exercises: Chapter 8 Problem 8.1, except part (d) Problem 8.2, only parts (a), (b) and (d) Problem 8.3 You will learn the following: • • • • • • • • • • • What is a dynamic game What is belief revision Two different ways of revising your belief What are conditional beliefs What does it mean to believe in the opponent's future rationality What is common belief in future rationality An algorithm to select those strategies that can rationally be chosen under common belief in future rationality How to apply this algorithm to examples What is a game with perfect information What is backward induction in games with perfect information That common belief in future rationality leads to backward induction Week 6: Strong belief in the opponent’s rationality Read: Chapter 9, Sections 9.1, 9.2 and 9.3 Exercises: Chapter 9 Problem 9.4, only (a), (b), (c) Problem 9.6, only (a), (b), (c) and (f) Extra exercise: see Canvas Hint to Problem 9.4: Model the dynamic game as follows (you still have to fill in the utilities): See Canvas You will learn the following: • • • • • What does it mean to strongly believe in the opponent's rationality How it is different from believing in the opponent's future rationality What is common strong belief in rationality An algorithm that can be used to find the strategies that you can rationally make under common strong belief in rationality How to apply this algorithm to examples Week 7: Economic applications of dynamic games Exercises: Problem set week 7, problems 1, 2 and 3. During the lecture we will first define the concept of subgame perfect equilibrium, which is often used in economic applications. We show that subgame perfect equilibrium is closely related to common belief in future rationality. We then apply the concepts of common belief in future rationality, subgame perfect equilibrium and common strong belief in rationality to economic models. In particular, we will look at: • • • a model of sequential pricing a model of alternative offers bargaining a firm entering a market You will learn the following: • • • How certain economic models can be translated into dynamic games How to apply the concepts of common belief in future rationality, subgame perfect equilibrium and common strong belief in rationality to these economic models Understand the strategic thinking of economic actors in dynamic situations
