625.741.81 - Game Theory

Expanded Course Description

Prerequisites: Multivariate calculus, linear algebra and matrix theory (e.g., EN.625.609 Matrix Theory), and a course in probability and statistics (such as EN.625.603 Statistical Methods and Data Analysis).

Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on the left menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates. 

Course Topics

• Strategic Games (Pure Strategies Only)
• Strategic Games Allowing Mixed Strategies
• Zero-Sum Games
• Finding All Nash Equilibria -- Theory and Algorithms
• Subgame Perfect Equilibria
• The Ultimatum Game and Bargaining
• Bayesian Games
• Signaling Games
• Cooperative Games

Course Goals

To gain a basic understanding of the language, concepts, and theoretic foundations for game theory, as well as to provide a survey of important theoretical models within the field.

Course Learning Outcomes (CLOs)

• To model certain types of human behavior in competitive decision-making situations.
• To determine and use appropriate solution techniques for our models of competitive decision-making problems.
• To have a solid understanding of the theoretical foundations for the fundamental models in game theory.

Textbooks

Osborne, Martin J. (2004). An Introduction to Game Theory. New York, NY: Oxford University Press.

ISBN-10: 0195128958 ISBN-13: 978-0195128956

Other Materials & Online Resources

Please make sure you have the appropriate prerequisite skills for this course. In particular, it is assumed that students are comfortable with multivariate calculus, basic linear algebra, and basic probability theory.  At a minimum, this includes:

1. calculation of limits
2. derivative definition as a limit
3. product rule for differentiation
4. L'Hopital's rule
5. chain rule for differentiation
6. integration by parts
7. integration via substitutions
8. partial derivatives
9. Gaussian/Gauss-Jordan elimination
10. Conditional probability
11. Bayes' Rule

Required Software

MATLAB

It is suggested that you obtain access to a recent version of Matlab. A license is provided at no cost to you, through JHU.

Visit the JHU IT Services Portal. Log in with your JHED ID and type “Matlab” in the search bar. Click on “Matlab for Students” in the search results and follow the instructions provided.

Student Coursework Requirements

It is expected that each module will take approximately 8–11 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 2-3 hours per week) as well as some outside reading, watching the lecture videos (approximately 2–3 hours per week), and writing assignments (approximately 4-5 hours per week).

This course will consist of the following basic student requirements:

Preparation and Participation (10% of Final Grade Calculation)
You are responsible for carefully reading all assigned material and being prepared for discussion. The majority of readings are from the course text. Additional reading may be assigned to supplement text readings.

Post your initial response to the discussion questions by the evening of day 7 for that module week. Posting a response to the discussion question is part one of your grade for module discussions (i.e., Timeliness).

Part two of your grade for module discussion is your interaction (i.e., responding to classmate postings with thoughtful responses) with your classmates (i.e., Critical Thinking). Just posting your response to a discussion question is not sufficient; we want you to interact with your classmates. Be detailed in your postings and in your responses to your classmates' postings. Feel free to agree or disagree with your classmates. Please ensure that your postings are civil and constructive.

I will monitor module discussions and will respond to some of the discussions as discussions are posted.

Evaluation of preparation and participation is based on contribution to discussions.

Preparation and participation is evaluated by the following grading elements:

1. Timeliness (50%)
2. Critical Thinking (50%)

Preparation and participation is graded as follows:

• 100–90 = A—Timeliness [regularly participates; all required postings; early in discussion; throughout the discussion]; Critical Thinking [rich in content; full of thoughts, insight, and analysis].
• 89–80 = B—Timeliness [frequently participates; all required postings; some not in time for others to read and respond]; Critical Thinking [substantial information; thought, insight, and analysis has taken place].
• 79–70 = C—Timeliness [infrequently participates; all required postings; most at the last minute without allowing for response time]; Critical Thinking [generally competent; information is thin and commonplace].

Assignments (30% of Final Grade Calculation)
All modules, except Modules 7 and 14, will contain a graded problem set. These assignments will be based on the theory and algorithms discussed in the associated module. Each assignment will have approximately 4 problems of varying difficulty. You are encouraged to collaborate (within the JHU guidelines on academic integrity) on these assignments.  Students may work in a team of up to 3 students.  Each student should assist in the solution of each problem.  One member of the team should submit an assignment for the team with each team member's name listed.  Each member of the team will receive the same grade on the assignment.

Direct copying of someone else’s written work or computer code is considered to be cheating and will result in a grade of zero on the assignment and a possible F in the course.

Usually you will be required to complete a problem “by hand.” This means that you should not use any specialized software to do the work. (However, there is no reason you cannot check your work with commercially available software, shareware, freeware, etc.) Some assignments will have a computing (Matlab) component that each student is encouraged to attempt, regardless of whether you are working in a team or not.

Graded assignments will be returned weekly, providing frequent feedback. Problem sets will be graded out of 100 points. The allocation of those points to specific problems may vary from assignment to assignment depending on the degree of difficulty. Partial credit may be given. For each individual item that is graded the following (approximate) rubric will be used:

• 100 – 90% of item’s total points: Very good to excellent work; 0-1 minor issues.
• 80 – 89% of item’s total points: Good work however there are some aspects that could be improved; 0-1 major issues and/or 2 or more minor issues.
• 70 – 79% of item’s total points: Satisfactory work. Student shows understanding of what needs to be done but there are multiple issues that need to be addressed; 2-3 major issues.
• 0 – 69% of item’s total points: Unsatisfactory work. (Includes lack of understanding of assignment, extreme carelessness, etc.).

All problem sets are due according to the dates in the Calendar.  Since the two lowest homework grades will be dropped, no late problem sets will be accepted.  (See the Homework/Project/Exam Submission Guide located in the Course Overview for additional details.) 

Exams (60% of Final Grade Calculation, combined from 30% for Midterm and 30% for Final)
There will be two exams given, one in Module 7 and the other in Module 14. Each of these exams will be timed and open book, with no collaboration allowed. The midterm exam (Module 7) will focus on the course material taught in Modules 1-6. The final exam (Module 14) will focus on the course material taught in Modules 8-13.

Both of these exams will provide you the opportunity to demonstrate your ability to determine the required techniques and apply them to solve game theory problems outside of the framework of a specific lecture/individual topic. Each of these exams will be worth 30% of your final grade

For each individual item that is graded the following (approximate) rubric will be used:

Exams are graded as follows:

• 100 - 90% of item's total points: Very good to excellent work; 0-1 minor issues.
• 80 - 89% of item's total points: Good work however there are some aspects that could be improved; 0-1 major issues and/or 2 or more minor issues.
• 70 - 79% of item's total points: Satisfactory work. Student shows understanding of what needs to be done but there are multiple issues that need to be addressed; 2-3 major issues.
• 0 - 69% of item's total points: Unsatisfactory work. (Includes lack of understanding of assignment, extreme carelessness, etc.).

Grading Policy

Assignments are due according to the dates posted in the course site. You may check these due dates in the Calendar or in the corresponding modules. I will post grades one week after assignment due dates. Graded work (with the exception of the final exam) will be returned to the student for review.

We generally do not directly grade spelling and grammar. However, egregious violations of the rules of the English language will be noted without comment. Consistently poor performance in either spelling or grammar is taken as an indication of poor written communication ability that may detract from your grade.

A grade of A-/A/A+ indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week.

A grade of B-/B/B+ indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.

A grade of C+ or lower indicates that the student has failed to show a graduate level of understanding of the course material.

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10). The following should be used as a general guideline on assignments to help determine your progress in the course:

Score Range	Letter Grade
100-98	A+
97-94	A
93-90	A-
89-87	B+
86-83	B
82-80	B-
79-77	C+
76-73	C
72-70	C-
69-67	D+
66-63	D
< 63	F

Final grades will be determined by the following weighting:

Item	Percent of Final Grade
Preparation and Participation	10%
Assignments*	30%
Exams (Midterm + Final)	60% (30% + 30%)

*The two lowest homework grades will be dropped, provided the grade is not a result of a violation of academic integrity policies.

Course Policies

Instructor Comments on Academic Dishonesty
The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse. The following list addresses some behaviors constituting academic dishonesty. This list is by no means intended to be comprehensive and is to be used in conjunction with JHU’s official Academic Misconduct Policy, which is described in the next section.

• In this course, you may collaborate with other students on homework and/or projects. However, you are ALWAYS to write up your solutions individually, even when you work in a group (unless otherwise instructed).
• Use of previous course material is prohibited (except as provided by the instructor). If you have questions about this policy, please ask the instructor.
• Use of solutions and instructor materials are ALWAYS prohibited.
• Posting of course materials to unapproved sites is prohibited.
• Students are reminded that misrepresenting information about their personal circumstances to a university official, including a faculty member, constitutes academic dishonesty and is grounds for action by the Academic Ethics Board.

If you are aware of any classmates involved in behavior of questionable ethics with regards to this class, you should contact the instructor immediately.

Any suspected violations of these policies will be reported.  If it is deemed that a violation has a occurred, the students involved may receive a grade of zero on the assignment/project/exam or possibly an F in the course.

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.