QSS/MATH 30.04: Evolutionary Game Theory and Applications

ORC Course Description: The course introduces basic concepts in evolutionary game theory, including evolutionarily stable strategies, replicator dynamics, finite populations, and games on networks, along with applications to social evolution, particularly to understanding human cooperation.

ORC Prerequisites for MATH 30:04: Math 20. The student should be familiar with calculus, and basic concepts in probability and ordinary differential equations. Programing skills helpful, but not required.

Suggested Textbooks:

Nowak, M. A. (2006). Evolutionary dynamics. Harvard University Press.

Sigmund, K. (2010). The calculus of selfishness. Princeton University Press.

Teaching Format:

Asynchronous remote teaching via pre-recorded lectures.

Virtual instruction via Canvas and Zoom available for remote participation.

Grading Formula:

The top priority of this course is your health and well-being. The class will ensure everyone be free of pressure and anxiety.
Four Homework Problem Sets (40%) + Final Essay (50%, an ~800-word essay (not longer than 1000 words) on topics of your choice that are related to mathematical humanities; I would like to encourage you to publish your essay in Medium.com as an original contributor, and list this on your CV) + Flash talk based on this essay (10%).

Optional for students interested in getting an academic Citation:
Elect to do a final project track in place of the final essay track. The final project requires a significant component of using quantitative methods (game theory models, statistical analyses, or simulations) as well as a final report (~15 pages) written in the format of a scientific paper.

Important Dates


Tentative lecture plan which may be subject to further changes.

Week Lecture Readings
Lec 1 Evolutionary Games: Introduction & Overview Nowak, M. A., & Sigmund, K. (2004). Evolutionary dynamics of biological games. Science, 303(5659), 793-799.
Lec 2 Stability Concepts: Nash Equilibrium vs. Evolutionarily Stable Strategy Smith, J. M., & Price, G. R. (1973). The logic of animal conflict. Nature, 246(5427), 15-18.
Lec 3 Replicator Equations and Its Connection with Ecological Dynamics Bomze, I. M. (1983). Lotka-Volterra equation and replicator dynamics: a two-dimensional classification. Biological cybernetics, 48(3), 201-211.
Lec 4 Social Dilemmas of Cooperation Kollock, P. (1998). Social dilemmas: The anatomy of cooperation. Annual Review of Sociology, 183-214.
Lec 5 Rules for Cooperation Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314(5805), 1560-1563.
Lec 6 Repeated Games Binmore, K. G., & Samuelson, L. (1992). Evolutionary stability in repeated games played by finite automata. Journal of Economic Theory, 57(2), 278-305.
Press, W. H., & Dyson, F. J. (2012). Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent. Proceedings of the National Academy of Sciences, 109(26), 10409-10413.
Lec 7 Beyond Pairwise Interactions: Multi-Person Games Hardin, G., (1998) Extensions of "the tragedy of the commons". Science, 280(5364): 682-683.
Lec 8 Spatial Games Nowak, M. A., & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359(6398), 826-829.
Lec 9 Adaptive Dynamics Dieckmann, U., & Law, R. (1996). The dynamical theory of coevolution: a derivation from stochastic ecological processes. Journal of Mathematical Biology, 34(5-6), 579-612.
Lec 10 Evolutionary Branching Hofbauer, J., & Sigmund, K. (2003). Evolutionary game dynamics. Bulletin of the American Mathematical Society, 40(4), 479-519.
Doebeli, M., Hauert, C., & Killingback, T. (2004). The evolutionary origin of cooperators and defectors. Science, 306(5697), 859-862.
Lec 11 Finite Populations I Nowak, M. A., Sasaki, A., Taylor, C., & Fudenberg, D. (2004). Emergence of cooperation and evolutionary stability in finite populations. Nature, 428(6983), 646-650.
Traulsen, A., Claussen, J. C., & Hauert, C. (2005). Coevolutionary dynamics: from finite to infinite populations. Physical Review Letters, 95(23), 238701.
Lec 12 Finite Population II Fudenberg, D., Nowak, M. A., Taylor, C., & Imhof, L. A. (2006). Evolutionary game dynamics in finite populations with strong selection and weak mutation. Theoretical population biology, 70(3), 352-363.
Lec 13 Evolutionary Graph Theory Lieberman, E., Hauert, C., & Nowak, M. A. (2005). Evolutionary dynamics on graphs. Nature, 433(7023), 312-316.
Ohtsuki, H., Hauert, C., Lieberman, E., & Nowak, M. A. (2006). A simple rule for the evolution of cooperation on graphs and social networks. Nature, 441(7092), 502-505.
Perc, M., & Szolnoki, A. (2010). Coevolutionary games--a mini review. BioSystems, 99(2), 109-125.
Lec 14 Vaccination Dilemma Bauch, C. T., & Earn, D. J. (2004). Vaccination and the theory of games. Proceedings of the National Academy of Sciences of the United States of America, 101(36), 13391-13394.
Lec 15 Evolutionary Dynamics of In-group Favoritism Masuda, N., & Fu, F. (2015). Evolutionary models of in-group favoritism. F1000Prime Reports, 7, 27.
Lec 16 Evolution of Homophily Fu, F., Nowak, M.A., Christakis, N.A., & Fowler, J.H.(2012) The evolution of homophily. Scientific reports, 2: 845.
Week 9 Final Project Presentations TBD

Course Projects and Presentation Schedule


Approximately 4 weeks are given to complete the final essey/final project. The instructor will suggest project ideas in the third week, but you are allowed to propose your own, which has to be approved by the instructor in the fourth week at the latest. Each essay/project presentation is limited to 10 minutes and preferably in the style of TED talks.

Presentation Schedule Download

Course projects are listed in the alphabetical order of student names, and will be updated once more progresses are made by the students.

Course Policies

Class Recording Notifications to Students

(1) Consent to recording of course meetings and office hours that are open to multiple students.

By enrolling in this course,
a) I affirm my understanding that the instructor may record meetings of this course and any associated meetings open to multiple students and the instructor, including but not limited to scheduled and ad hoc office hours and other consultations, within any digital platform, including those used to offer remote instruction for this course.
b) I further affirm that the instructor owns the copyright to their instructional materials, of which these recordings constitute a part, and my distribution of any of these recordings in whole or in part to any person or entity other than other members of the class without prior written consent of the instructor may be subject to discipline by Dartmouth up to and including separation from Dartmouth.

(2) Requirement of consent to one-on-one recordings

By enrolling in this course, I hereby affirm that I will not make a recording in any medium of any one-on-one meeting with the instructor or another member of the class or group of members of the class without obtaining the prior written consent of all those participating, and I understand that if I violate this prohibition, I will be subject to discipline by Dartmouth up to and including separation from Dartmouth, as well as any other civil or criminal penalties under applicable law. I understand that an exception to this consent applies to accommodations approved by SAS for a student’s disability, and that one or more students in a class may record class lectures, discussions, lab sessions, and review sessions and take pictures of essential information, and/or be provided class notes for personal study use only.

If you have questions, please contact the Office of the Dean of the Faculty of Arts and Sciences.

Honor Principle

Collaborations (giving and receiving assistance) during closed-book exams and quizzes are strictly prohibited. Any form of plagiarism is not allowed in the final project. If you have questions, please ask the instructor before doing and should always refer to Academic Honor Principle.

Student Accessibility and Accommodations

Students requesting disability-related accommodations and services for this course are encouraged to schedule a phone/Zoom meeting with the instructor as early in the term as possible. This conversation will help to establish what supports are built into the course. In order for accommodations to be authorized, students are required to consult with Student Accessibility Services (SAS; Getting Started with SAS webpage; student.accessibility.services@dartmouth.edu; 603-646-9900) and to request an accommodation email be sent to the instructor. We will then work together with SAS if accommodations need to be modified based on the learning environment. If students have questions about whether they are eligible for accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.

Student Religious Observances

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with the instructor before the end of the second week of the term to discuss appropriate accommodations.

Mental Health and Wellness

The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean, Counseling and Human Development, and the Student Wellness Center. The instructor would like to encourage you to use these resources to take care of yourself throughout the term, and to come speak to the instructor if you experience any difficulties.

Late Policy

As we are amid once-in-a-century pandemic, please request approporiate accommodations if you expect delays in turning in your assignments. Otherwise, by "deadline" we really mean it. On the condition of accepting the penalty for turning in the final project report late (that is, 5% each additional day), however, an extension of maximum 4 days will be granted on a case-by-case basis. In exceptional circumstances, students with disabilities should inform the instructor of their accommodation requests well in advance, so that the instructor will have sufficient time to work with Student Accessibility Services to provide appropriate accommodations.