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Evolutionary Game Theory and Applications
Program Overview
QSS/MATH 30.04: Evolutionary Game Theory and Applications
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.
Prerequisites
- Math 20
- Familiarity with calculus, basic concepts in probability, and ordinary differential equations
- Programming skills are 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.
Important Dates
- Final project proposal due on: 12 April 2024
- Homework problem sets due biweekly
- Final project presentations: in the week of 20 May 2024 (Week 9)
- Participation of Dartmouth Mathematics Undergraduate Poster session: 28 May 2024, 2-4pm Kemeny/Haldeman Hallway
- Final project report due on: 31 May 2024
- Course withdrawal deadlines:
- 6 May 2024: Final day for dropping a 4th course
- 15 May 2024: Final day to withdraw from a course
Syllabus
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). |
| 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. |
| 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. |
| 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. |
| 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. |
| 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). |
| 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
Projects
Approximately 5 weeks are given to complete the 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. Project presentation is limited to 10 minutes and preferably in the style of TED talks.
Course Policies
Class Recording Notifications to Students
By enrolling in this course, students affirm their understanding that the instructor may record meetings of this course and any associated meetings open to multiple students and the instructor.
Honor Principle
Collaborations during closed-book exams and quizzes are strictly prohibited. Any form of plagiarism is not allowed in the final project.
Student Accessibility and Accommodations
Students requesting disability-related accommodations and services for this course are encouraged to schedule a meeting with the instructor as early in the term as possible.
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, 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.
Late Policy
As we are amid a national mental health crisis, please request appropriate 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.
