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 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)

Questions

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