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Consider the following situation:

  • A population of students is working on group projects. Students can follow two strategies (\(S\)): work hard for the project or free-ride.
  • In every course, groups of size n are formed at random. Students use the strategy determined at the beginning of the course (see below). This is the semester
  • Total group effort is determined by the composition of the group. In a group with \(h\) hard workers and \(l=n-h\) lazy workers total group effort is \(e=h*H+l*L\) (\(H\) and \(L\) being the effort put in by hard/lazy workers)
  • When group projects are marked, every student gets the same mark. The lecturer determines this mark as \(m=e/n\) (i.e. the larger this number the better the mark) \(n\) is the number of students in a group

  • At the end of the semester students rethink their strategies. They do this, by selecting another student at random and comparing a measure based on marks and effort, \(m-a*S\) (where \(a\) is a parameter and \(S=H\) or \(S=L\) depending on strategy). If that student got a measure, they will follow his strategy in the next semester.

  • Students study forever (i.e. take an infinite number of courses)


  • Assuming we start with equal numbers of hard-working and lazy workers, what is the composition of the group

    • After 4 years (i.e. 8 courses) if H=1 and L=0 and a=0.5.
    • in the long run (after an “infinite” number of years)?
    • How quickly is this equilibrium state reached?
  • How do the following parameters influence results:

    • Initial composition of the group
    • Group size (\(n\))
    • Cost of effort \(a\)
    • Contribution of hard workers to group effort (i.e. \(H\) and \(L\))


  • Have to write own numerical solving code
    • Implement Euler method?
    • Could initially try with something that scipy exposes?


This is done via a report handed in on the 17th May 2024. This report should include the following:

  • Give a description of the problem
  • Document the analytical approach to solving it
  • Document the application of numerical integration methods
    • This must be created ourselves in a 'low-level' language
    • Need choices of parameters for solver and explain why
    • Document and discuss comparisons
  • Agent based model of the simulation
    • Discuss how implemented
    • Discussion of results and comparisons
  • Style is conference paper
  • Give some extension to the model and try to convince Markus that it is an interesting extension, in such a way that it can be reproduced

Evolutionary game theory group coursework