Evolutionary Game Theory: Math 697EG

Meeting : TuTh 1:00--2:15    LGRT 115

Instructor : Luc Rey-Bellet

 Office :   1423 J LGRT
 Phone :  545-6020
 E-Mail :  luc@math.umass.edu
 Office Hours :   Tu 10:30--12:00,   Th 2:45--4:00,   or by appointment.

Homework:

• Homework 1 and Solutions
• Homework 2 and Solutions
• Homework 3

Classnotes: Some (partial) classnotes will be posted and regularly updated here

References: I will not follow any textbook very closely. You are however very strongly encouraged to consult textbooks on your own.

The first three books are texts about evolutionary game theory and cover most of the class material.

• Evolutionary Game Theory, Jorgen W. Weibull, MIT Press. ( In reserve at the library)
  
  
• Evolutionary games and population dynamics, Josef Hofbauer and Karl Sigmund. Cambridge University Press, 1998. ( In reserve at the library)
  
  
• Population Games and Evolutionary Dynamics William H. Sandholm, MIT Press (to be published) ( The book is not published yet but a preliminary version is accessible courtesy of the author (ask me and I will send you the .pdf file) )
  
  

• Game theory, James N. Webb, Springer Undergraduate Series ( Online version accessible at the online Springer collection (UMass NET ID needed)
  
  
• Game Theory, by Hans Peters, Springer. ( Online version accessible at the online Springer collection (Umass NET ID needed)
  
  
• Game Theory: Analysis of Conflict, Roger B. Myerson, Harvard University Press. ( In reserve at the library)
  
  

Syllabus: This course is an introduction to evolutionary game theory. Prerequisites are a working knowledge of differential equations as well as basic probability theory. No previous knowledge of game theory is required.
In standard game theory players can choose between different strategies, each strategy yields a payoff which depends on the strategies chosen by the other player(s). The central concept is the static concept of Nash equilibrium where no player has incentive to change his strategy choice. Evolutionary game theory was invented by biologists (and economists) to describe evolutionary selection process. Here players are drawn at random and are given a chance to update strategies. The updating mechanism (aka learning mechanisms) are various depending on the assumptions on players. One of the goal is to select/justify the static equlibrium concept via this dynamical approach. The applications of evolutionary games are numerous, for examples in biology, computer sciences, economics, and physics.
In the class we will first introduce the basics of static, non-cooperative game theory and discuss some of the concepts of equilibria. We then introduce and discuss dynamical approaches both using differential equations and simple stochastic models. Numerous examples will be discussed in detail.

Grade: Homework will be assigned on a regular basis. Each student will pick a project of his choice (under my supervision). I expect a written project at the end of the semester and each student will give an oral presentation to the class.