MATH 76.01: Evolutionary Game Dynamics

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

Prerequisites: Math 22, Math 23. The student should be familiar with calculus, and basic concepts in ordinary differential equations and probability. Programing skills highly recommended, but not required.

Textbook: Nowak, M. A. (2006). Evolutionary Dynamics. Harvard University Press.

Grading Formula: (i) Attendance & Participation (10%) + (ii) Homework Problem Sets (40%) + (iii) Final Project Proposal (10%) + Final Project Report (30%) + Final Project Presentation (10%).

Important Dates


Tentative lecture plan which may be subject to further changes.

Date Lecture Readings
5 January 2017 Evolutionary Games: Introduction & Overview Nowak, M. A., & Sigmund, K. (2004). Evolutionary dynamics of biological games. Science, 303(5659), 793-799.
10 January 2017 Stability Concepts: Nash Equilibrium vs. Evolutionarily Stable Strategy
12 January 2017 Replicator Equations and Its Connection with Ecological Dynamics
17 January 2017 Social Dilemmas of Cooperation Kollock, P. (1998). Social dilemmas: The anatomy of cooperation. Annual Review of Sociology, 183-214.
19 January 2017 Rules for Cooperation Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314(5805), 1560-1563.
24 January 2017 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.
26 January 2017 Spatial Games Nowak, M. A., & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359(6398), 826-829.
31 January 2017 Final project proposal due
31 January 2017 Beyond Pairwise Interactions: Multi-Person Games Hardin, G., (1998) Extensions of "the tragedy of the commons". Science, 280(5364): 682-683.
2 February 2017 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.
7 February 2017 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.
9 February 2017 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.
14 February 2017 Finite Population II
February 2017 Final day for dropping a fourth course
16 February 2017 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.
20 February 2017 Final day to withdraw from a course
21 February 2017 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.
23 February 2017 Evolutionary Dynamics of In-group Favoritism Masuda, N., & Fu, F. (2015). Evolutionary models of in-group favoritism. F1000Prime Reports, 7, 27.
28 February 2017 Evolution of Homophily Fu, F., Nowak, M.A., Christakis, N.A., & Fowler, J.H.(2012) The evolution of homophily. Scientific reports, 2: 845.
2 March 2017 Final Project Presentations Day I
7 March 2017 Final Project Presentations Day II
8 March 2017 Final project report due

Course Projects and Presentation Schedule


Approximately 4 weeks are given to complete the 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 project presentation is limited to 15 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.

Name Project Title
Paula X. Chen'17
Liane E. Makatura'17
Modeling the Spread of Fake News in Spatial Populations
Madeleine M. Cooney'17
Milan P. Huynh'17
Adaptive Networks and Wealth Dependent Strategies - A Model for Successful Altruism
Rachel R. Patel'17
Danielle W. Kimball'17
Cooperative Dynamics of Yeas
Tucker E. Evans'19 Why do they not believe? - The Network Dynamics of Opinion
Julio A. Resendiz'17
Luis F. Marin'17
An Evolutionary Game-Theoretic Analysis of Dice Strategies
Goodwill M. Batalingaya'16 Public Goods Games: Social Welfare Programs & Wealth Accumulation
Dale T. Clement'17 The Adaptive Dynamics of Evolutionary Trapping and Rescue
Peter S. Wang'17 Evolutionary Game Dynamics in Super Smash Bros. Melee
John R. Lewis III'17 The Population Problem of Antibiotic Overuse
Daniel Huang’17 Strategic Risk Management of Financial Assets
Andrew D. Dixon'17 Does It Really Pay to Use Growth Promoters in Farming Industry?

Course Policies

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.

Accessibility Policy

Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see your instructor before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested. At such a meeting please provide your instructor with a copy of a disability registration form, which lists the accommodations recommended for the student by Student Accessibility Services within the Academic Skills Center. The person you might want to contact at the Academic Skills center is Ward Newmeyer, Director of Student Accessibility Services 205 Collis Center - (603) 646-9900.

Student Religious Observances

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

Late Policy

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.