Economics 326h5s
Instructor: Carolyn Pitchik
Syllabus
Canvas course web page
- Please note that there will be information posted on Canvas as well as information posted on this course website.
- Please see the Canvas course web page to find out how to access the lecture notes and past tests on this course website.
What's new? (most recent at top)
12/12/2021 Please see below for fourth and fifth Announcements about the final exam: More to come
02/12/2021: Please see below for Expanded Lecture 12
25/11/2021: Please see below for Expanded Lecture 11
25/11/2021: Please see below for first, second, and third announcements regarding the Final Exam- More to come
18/11/2021: Please see below for Expanded Lecture 10
15/11/2021: Please see below for announcement regarding the make-up test
11/11/2021: Please see Expanded Lecture 9 below
11/11/2021: Please see below for Questions from Previous Tests and Exams + Solutions (questions from chapters 5-6-7-16)
11/11/2021: Please see below for Questions from Previous Tests and Exams + Solutions (questions from chapter 9)
04/11/2021: Please see Expanded Lecture 8 below
29/10/2021: Please see Expanded Lecture 7 below
29/10/2021: Please see below for Solutions to Test #1
09/10/2021: Please see Expanded Lecture 6 below for some approaches to finding NE and for solutions to selected textbook exercises in Chapters 1-4
08/10/2021: Please see Expanded Lecture 5 below
06/10/2021: Please see below for an announcement regarding tips for studying for the Term Test
06/10/2021: Please see below for an announcement regarding tips for writing the Term Test
06/10/2021: Please see below for Announcements 1-2-3 regarding the Term Test
02/10/2021: Please see below for Solutions to Questions from Previous Tests and Final Exams (questions from chapters 1-2-3-4)
02/10/2021: Please see below for a Compilation of Questions from Previous Tests and Exams based on chapters 4
02/10/2021: Please see below for a Compilation of Questions from Previous Tests and Exams based on chapters 1-2-3
02/10/2021: Please see Expanded Lecture 4 below
24/09/2021: Please see Expanded Lecture 3 below
17/09/2021: Please see Expanded Lecture 2 below
09/09/2021: Please see Expanded Lecture 1 below
09/09/2021: Please see below for on-line Solutions to Selected Exercises in An Introduction to Game Theory by Martin J. Osborne
24/08/2021: Please see above for the current course syllabus
Announcement regarding Make-Up Test
- The make-up test for the term test is scheduled to start at 5 p.m. on Monday 6 December 2021
- Those who missed a term test will automatically get zero unless they write the make-up
- You may NOT use your final exam grade for a term test that you have missed
- Only eligible students are allowed to write the make-up test
- Anyone who is eligible for the Make-up Test should have received an email from me
- Any eligible student who was not contacted by me should email me as soon as possible
- There are no aids allowed on the make-up test
- You are responsible for all the material from the entire course
First Announcement for Final Exam: Exam Topics
- You are responsible for all the material covered in the
LECTURES and in the TEXTBOOK for the topics in Chapters 1-7, 9 and 16
and some topics in Chapter 10 on the syllabus
- If the topic appeared in class, or in the lectures, or in a text chapter, then you are responsible for it.
- The list of topics include (AT A MINIMUM), the following list. There may be other topics. When in doubt, consult the syllabus.
- You are responsible for the list of topics covered for test #1 and the topics covered after test #1
- You are responsible for finding the solution to a game that is
presented to you in either strategic form with or without chance moves with or without perfect information or in extensive form with perfect
information with or without chance moves and for games that are hybrids of extensive, strategic or Bayesian games.
- You are responsible for being able to formulate a game given a word problem and then solving it.
- You are responsible for the concepts of Nash equilibria (pure
and mixed non-pure NE), NE payoffs, subgame perfect Nash equilibria (pure and mixed non-pure SPNE), SPNE path, SPNE payoffs, Bayesian Nash equilibria
(pure and mixed non-pure BNE), and BNE payoffs
- You are responsible for knowing how to derive all solutions to a game
- You are responsible for knowing how to derive a pure NE and its associated NE payoffs
- You are responsible for knowing how to derive a mixed non-pure NE and its associated NE payoffs
- You are responsible for knowing how to derive a pure SPNE, a pure SPNE path and associated SPNE payoffs
- You are responsible for knowing how to derive a mixed non-pure SPNE, a SPNE lottery over terminal paths and associated SPNE payoffs
- You are responsible for knowing how to derive a pure BNE, and associated BNE payoffs in a Bayesian strategic game
- You are responsible for knowing how to derive a mixed non-pure BNE, and associated BNE payoffs in a Bayesian strategic game
- You are responsible for knowing how to derive a pure PNE and a mixed non-pure PBE, and associated BNE payoffs
- Know how to show a pure or mixed non-pure strategy (weakly or strictly) dominates another pure or mixed non-pure strategy
- Know when and how to use strict domination to reduce the size of a game in the search for Nash equilibria.
- Know how to perform comparative statics on the Nash equilibria (NE, SPNE, BNE) of a game
- Know how to use the best response functions to form equations to derive the pure Nash equilibria of a game with a continuum of actions and continuous and possibly kinked payoff functions
- Know how to derive the Nash equilibria of a game by considering different categories of action profiles in turn
- Know how to derive the Nash equilibria of a game by using a combination of properties of the best response functions and a consideration of classes of action profiles
- Know how to derive the Nash equilibria of a game by using the payoff function or the best response function to figure out properties of the action profile that must hold in a Nash equilibrium
- Know how to figure out properties of the action profile that may aid in finding the Nash equilibria
- Know how to derive the mixed (non-pure) Nash equilibria of a game with any
finite number of individuals, each of whom use a mixed strategy over a finite number of actions.
- Know how to set up a game theoretic model in strategic form from a story as is done for example, in the expert diagnosis game
- Know how to compare two different sets of Bernouilli utility
gambles functions to see whether they represent a common set of preferences over
- You are responsible for pure and mixed Nash equilibria of the
examples and exercises in the text including those in chapters 1-3
- You are responsible for pure and mixed Nash equilibria of the examples and exercises in chapter 4
- You are responsible for pure and mixed Nash equilibria and subgame perfect
Nash equilibria in extensive form games covered in Chapters 5, 6 and 7
- You can test yourself on word problems for Chapter 6 by trying the examples and questions in chapter 7
- You are responsible for Bayesian Strategic Games covered in Chapter 9 and Bayesian Extensive Games covered in Chapter 10
- You are responsible for Bargaining in Chapter 16 (including the limit of finite horizon bargaining games and variations of bargaining)
- You are responsible for solving a new game using any of the techniques used in the relevant book chapters, lectures, tests and exams
- You are responsible for knowing the set-up of the models (for example including but not limited to public good provision, auctions and bargaining)
- You are responsible for knowing how to derive the solution to a combination of models (for example including but not limited to combining say auctions and bargaining)
- You are responsible for knowing how to derive the solution to a model with a combination of game forms (for example including but not limited to combining say an extensive form game and chance moves (like the Bayesian variation of either Rubinstein bargaining or Stackelberg or Cournot) or an extensive form game with a strategic form game
- You are responsible for performing comparative statics on any of the solution concepts applied to any of the models or combination of models or model variations
There is an unlimited number of questions that can combine bits of several models or games.
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Second Announcement for Final Exam: Tips on how to study
- First study a chapter and test yourself with the chapter questions
- When you compare your answer with that given in the solutions
you can then decide whether you need to study further or whether you
should try some of the test questions
- Test yourself with some of the questions from past tests regarding the chapter
- When you compare your answer with that given in the solutions
you can then decide whether you need to study further or whether you can
continue to the next chapter
- If your answer is at odds with the one provided, try to see what aspect of the problem you didn't understand
- If your answers do not agree with the solutions provided,
figure out why and study further on that topic, then test yourself again
using past test questions.
- If your answers do agree with the solutions provided, then go
on to the next chapter and test yourself on questions from the chapter
and then on questions from past tests regarding this chapter
- Once you have finished each chapter, test yourself further by trying some of the final exam questions.
- If your answers do not agree with those given then you need to study further
- If your answers agree with those given then you are ready to sit down and take a practice exam by using a past exam.
- Use all questions in the text and on-line as a means to test your understanding of the material
- When reading the material, try to categorize the models into different types: # of players, # of actions, preferences
- When tackling a question, try to categorize the questions into different types
- When tackling a question, try to match the solution method to the model category
- You can also try and make up your own questions by mixing and matching ideas and models
- Try formulating and solving your own games
Third Announcement for Final Exam: Tips on how to write the final exam
- Remain Calm
- Do not panic because your mind is blank, Instead, relax and stay calm until the panic passes
- Budget your time
- Begin questions or parts of questions that you know how to answer
- If you get stuck on a question or part then go to another question or part that you do know how to solve
- If you cannot answer the question as posed in general then try to obtain part marks for answering a simpler version
(say n=2 or n=3 rather than general n for example)
- Explain your reasoning in your answers
- Try explaining what you would do generally then do it specifically for the question at hand
- Since we have discussed mixed behavioral strategies in a mixed SPNE only in the last few years note that even though past tests and exam questions prior to 2012 that ask about ALL SPNE were asking about ALL PURE SPNE (unless explicitly stated otherwise)
- Remember that new questions may arise as new material may be taught so that you may
need to think about how to do a question that has never been asked in any previous test or final exam
Fourth Announcement for Final Exam: Exam Schedule and Format
- For the exam date and time please refer to Final Exam Schedule
- The Final Exam will be held on Zoom (check Quercus for Zoom invite which differs from the class or office hour invites) on Tuesday 21 December 2021
- Final Exam Zoom Invitation and Instructions will be announced on Quercus on or prior to Friday 17 December 2021
- Please upload material for the Final Exam Honor Code assignment assessment in Crowdmark prior to elevan a.m. on Tuesday 21 December 2021
- There are 6 main questions on the final exam, each with one or two parts. Each main question is worth 17 marks.
- There are NO AIDS ALLOWED.
Fifth Announcement for Final Exam: OFFICE HOURS for FINAL EXAM with Zoom links and email addresses available on Quercus
- CP (using CP's Zoom office hour link for ECO 326): Mon, Dec 13th: 10AM - 12PM EST; Wed, Dec 15th: 10AM - 12PM EST
- AB (using AB's Zoom office hour link for ECO 326): Thu, Dec 16th: 7PM - 9PM EST; Mon, Dec 20th: 7PM - 9PM EST
- lf any of the above office hour time slots do not work for you, send AB an email (with ECO 326 Office Hour in the subject matter) to try and work out a different time to meet.
- If you prefer to communicate by email, CP will answer questions about the course material that are emailed to CP (with a short description of the question in the subject matter) on or before 5p.m. EST Sunday 19 December
Tips regarding studying for the test
- Make sure that you understand the concepts as well as the process of finding solutions.
- Make up your own questions. Each question is a test of your understanding of concepts.
- Learn all available methods so as to be able to apply the appropriate method to any particular problem
- You may be asked new questions that require you to match the appropriate solution method.
- Use all questions in the text (See Syllabus Outline for lists of questions in text) and this on-line webpage as a means to test your understanding of the material
- If your answer is at odds with the one provided, try to see what aspect of the problem you didn't get
- When reading the material, try to categorize the models into different types: # of players, # of actions, preferences
- When tackling a question, try to categorize the questions into different types
- When tackling a question, try to match the solution method to the model category.
- When tackling a question, think about using best response functions.
- When tackling a question, consider using different classes of action profiles.
When tackling a question, ask yourself whether it is better to use a combination of best response functions and action profile classes?
Tips regarding writing Test 1
- Remain calm
- Do parts that you recognize first
- Leave harder parts for later
- Keep track of # of players (finite or not; known or unknown), # of actions (finite or not; known or unknown), preferences (descriptions, utility numbers or functions)
- Keep in mind the definitions of Nash equilibrium (for pure and non-pure), strict and weak dominance
- When tackling a question, figure out the category then match the solution method to the model category
- Think about what intuition might help you solve the problem
- Remember that you have to derive the solution to each question. That is, you need to apply the right proces and show how it is used to derive the amswer to each question.
Announcement 1 regarding Test 1
- You are responsible for ALL the material in chapters 1-4 of
the textbook
- You are responsible for ALL the material in expanded lectures 1-6 and synchronous OneNote lectures 1-6
covering chapters 1-4 plus all extensions that we covered in class
- You are responsible but NOT LIMITED TO being able to perform various tasks including
- Know how to show a pure or mixed strategy (weakly or strictly) dominates another pure or mixed strategy
- Know how to show whether there exists a pure or mixed strategy (weakly or strictly) that dominates another
pure or mixed strategy
- Know when and how to reduce the size of an arbitrary sized matrix game in the search for Nash equilibria.
- Know how to find pure or mixed Nash equilibria of a two person matrix game of any size
- Know how to perform comparative statics on the Nash equilibria of any game that can be solved using the techniques discussed in class
- Know how to use the best response functions or the properties of a Nash equilibrium to form equations or inequalities to find the pure Nash equilibria of a
game with a continuum of actions and continuous, possibly kinked (i.e. piecewised defined) payoff functions
- Know how to find the Nash equilibria of a game by considering different action/strategy profiles or properties of action/strategy profiles in turn
- Know how to find the Nash equilibria of a game by using a combination of properties of the best response
functions and a consideration of classes of action/strategy profiles
- Know how to find the Nash equilibria of a game by using the payoff function or the best response function
to figure out properties of the action/strategy profile that must hold in a Nash equilibrium
- Know how to figure out properties of the action/strategy profile that may aid in finding the Nash equilibria
- Know how to reduce the set of candidate action/strategy profiles using strict domination when finding the set of (pure and mixed) Nash equilibria when condition R holds
- Know how to find the Nash equilibria of a game with any
finite number of individuals, each of whom use a mixed strategy over at least two
actions.
- Know how to check whether a given strategy profile (with pure or non-pure strategies) is a
Nash equilibrium of a given game.
- Know how to set up a game theoretic model in strategic form from a story as is done
for example, in the expert diagnosis game or the model of reporting a crime (or any of its variations) or the Cournot oligopoly model and many other models
- Know how to compare two different sets of Bernouilli utility
functions to see whether they represent a common set of preferences over
gambles
- Know how to solve the exercises given in chapters 1-2-3 and 4 specified in the Syllabus
- Know how to solve the problems given on the course web
page that cover chapters 1-2-3 and 4 including strict and weak
domination of mixed strategies
- Know how to adapt solutions to apply to new problems.
Announcement 2 regarding Test 1
- Test #1 will be held on Zoom on Friday 22 October 2021
- Test #1 Zoom Invitation will be announced prior to Friday 22 October 2021
- Please read the instuctions below very carefully well before Friday 22 October 2021
- Instructions for Test #1
Announcement 3 regarding Test 1 format
- Please upload material for the Honor Code assignment assessment in Crowdmark prior to 9 a.m. on Friday 22 October 2021
- Please see instructions for the test below with heading "New Announcement regarding Test 1" which appears just above the Extended Lectures
- Test #1 will be held on Zoom (check Quercus for Zoom invite which differs from the class or office hour invites) on Friday 22 October 2021
- There are NO AIDS ALLOWED.
- There are three questions on the test. Each question has three parts.
- I would like to give ample time to complete the test. The time you get will depend on how quickly we can process everyone
- Please do your best at setting up your camera position so as not to waste your time being processed during the test itself
Solutions to Exercises (PDF files for students with access to Adobe Reader)
The material below is accessible only to students in the course.
All material copyright © 1997-2021 Carolyn Pitchik
Expanded Lectures (PDF files for students with access to Adobe Reader) Not guaranteed to be complete or correct
Compilation of Questions from Previous Tests and Exams (arranged according to chapters)
Solutions to Previous Tests and Exams (not arranged according to chapter) (Solutions not guaranteed to be correct)