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.
Nowak, M. A. (2006). Evolutionary dynamics. Harvard University Press.
Sigmund, K. (2010). The calculus of selfishness. Princeton University Press.
Asynchronous remote teaching via pre-recorded lectures.
Virtual instruction via Canvas and Zoom available for remote participation.
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.
Tentative lecture plan which may be subject to further changes.
|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|
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.
Course projects are listed in the alphabetical order of student names, and will be updated once more progresses are made by the students.
(1) Consent to recording of course meetings and office hours that are open to multiple students.By enrolling in this course,
(2) Requirement of consent to one-on-one recordingsBy 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.