Coursework
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 freeride.
 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 \(l=nh\) 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, \(ma*S\) (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)
Questions

Assuming we start with equal numbers of hardworking 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 \(L\))
Gotchas
 Have to write own numerical solving code
 Implement Euler method?
 Could initially try with something that
scipy
exposes?
Assessment
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 'lowlevel' 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