Program Overview

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Program 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.

Grading Formula

• Four homework problem sets (40%)
• Final projects (40%) on topics of your choice
• Participation in Poster session (10%)
• Lightening talk based on this project (10%)

Final Project Requirements

• Significant component of using quantitative methods (including not limited to game theory models, statistical analyses, or simulations)
• Final report (~12 pages, single-spaced with font size 12 point) written in the format of a scientific paper
• Includes title, authors, abstract, introduction, model and methods, results, discussions, and conclusion along with references

Integration of ChatGPT

• The class welcomes the wise and responsible use of ChatGPT, or Large Language Models (LLMs) more generally, as an integral part of our experiential learning
• No penalty for utilizing ChatGPT, but explicit disclosure by including the prompt history as part of your submission is required

Instructor and Office Hours

• Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
• Registrar Scheduled Course Time: Section I: 10A, Section II: 2A
• Office Hours: TBD and by appointment
• Office: Feng Fu (210 Kemeny Hall)

Important Dates

• Final project proposal due on: 18 April 2023
• Homework problem sets due biweekly
• Final project presentations: in the week of 22 May 2023 (Week 9)
• Participation of Dartmouth Mathematics Undergraduate Poster session: 30 May 2023
• Final project report due on: 31 May 2023
• Course withdrawal deadlines:
  • 8 May 2023: Final day for dropping a 4th course
  • 17 May 2023: 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.

Course Projects and Presentation Schedule

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

• Consent to recording of course meetings and office hours that are open to multiple students.
• Requirement of consent to one-on-one recordings.

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.

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.

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.

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, so that the instructor will have sufficient time to work with Student Accessibility Services to provide appropriate accommodations.