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:
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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:
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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:
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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:
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price competition between firms that offer differentiated goods
competing firms that must choose their product characteristic
You will learn the following:
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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:
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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:
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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:
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a model of sequential pricing
a model of alternative offers bargaining
a firm entering a market
You will learn the following:
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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