Program Overview

---

QSS 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.

Teaching Format

The course is mainly lecture-based, supplemented by occasional group discussions and hands-on demos. Virtual instruction via Canvas and Zoom is available for remote participation.

Grading Formula

• Credit or No Credit: Turning in biweekly Homework Problem Sets
• Academic Citation: Completing a comprehensive Final Project and 15-minute Presentation

Instructor and Course Details

• Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
• Course Time: 10A TuThu 10:10am-12:00pm (x-hour Wed 3:30pm-4:20pm)
• Physical classroom: 028 Haldeman Hall

Important Dates

• Final project proposal due on: 21 April 2020
• Homework problem sets due biweekly
• Final project presentations: in the week of 25 May 2020 (week 9)
• Final project report due on: 5 June 2020
• Course withdrawal deadlines:
  • 11 May 2020: Final day for dropping a 4th course
  • 20 May 2020: Final day to withdraw from a course

Syllabus

Tentative Lecture Plan

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.
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), .
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), .
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), .
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 4 weeks are given to complete the project. The instructor will suggest project ideas in the third week, but students are allowed to propose their own, which must 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.

Course Policies

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 with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see the instructor privately 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 a religious observance conflicts with 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 student life. There are resources available on campus to support wellness, including the undergraduate dean, Counseling and Human Development, and the Student Wellness Center.

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.