[Tutorial]: Congestion and weighted congestion games

[rahulsavani]

Describe the tutorial you want to see.

Congestion games always have pure equilibria ,via a potential function argument. On the other hand weighted congestion games may not have pure equilibria, but of course will have mixed equilibria.

A tutorial that introduced these games and gave small examples, e.g. with only two players for the simplest case, could be used to demonstrate the above facts, while using enumpure_solve (for 2 or more players) and enummixed_solve (for the 2 player case, including an example of a 2 player weighed congestion game and it's corresponding bimatrix game that has no pure equilibrium, which can also demonstrate iterated elimination of strictly dominated strategies).

The tutorial can also briefly discuss "potential games", of which congestion games are an example.

Who is the tutorial for?

Undergrad/grad students of game theory, in particular those studying algorithmic game theory, where congestion games often feature.

Add links to papers and software.

Here is an extract from an exercise sheet I wrote that provides the mentioned bimatrix examples:

[hriztam]

Hello @rahulsavani , if this issue is still open, I would like to help with this

[khushthecoder]

Hi @rahulsavani, I would love to take this on for GSoC 2026! I'm putting together a Jupyter notebook now that walks through the specific 2-player example you provided.

My plan is to structure it pedagogically:
Formulating the unweighted case and using pygambit.nash.enumpure_solve to demonstrate the guaranteed pure NE via the potential function argument.
Formulating the weighted case ($w_1=1, w_2=2$) to show the absence of pure NE.
Passing the weighted case to pygambit.nash.enummixed_solve.
Demonstrating the iterated elimination of strictly dominated strategies on the bimatrix.
I can have a draft PR up shortly if you're happy for me to proceed with this structure!