[Tutorial]: SageMath interoperability tutorial

[edwardchalstrey1]

Describe the tutorial you want to see.

Add a tutorial demonstrating interoperability of SageMath & Gambit. This can initially just be:

1. Load some normal form games from the SageMath catalog in Gambit
2. Use Gambit to compute equilibria

Later on, if there is a deeper connection between SageMath & Gambit, this tutorial can be updated. See previous effort at integration.

Who is the tutorial for?

New users to Gambit and SageMath who have basic Python programming skills:

• can assume user is familiar with intro tutorials 1-3
• no particular advanced game theory knowledge

Add links to papers and software.

• SageMath Parser For gambit And lrs Nash Equilibria
• SageMath catalog of normal form games

[edwardchalstrey1]

Note that the Normal form games with N players SageMath guide actually does some of the above in addition to calling Gambit directly to use the LCP solver. See "It is also possible to generate a Normal form game from a gambit Game" on that page.
Updating this guide (to use pygambit v16) is part of what sagemath/sage#37809 is doing. So it may be worth working on that PR in tandem with this tutorial to avoid duplication. Perhaps if the SageMath page post-refactoring is sufficiently detailed we should link to it from the Gambit docs instead of adding a new tutorial.

There is also a paragraph that says:

For more information on using Gambit in Sage see: Using Gambit in Sage. This includes how to access Gambit directly using the version of iPython shipped with Sage and an explanation as to why the int calls are needed to handle the Sage preparser.

... however this page doesn't seem to exist.

[edwardchalstrey1]

• Related issue: Gambit Integration into SageMath alan-turing-institute/gambit_admin#3
• Gambit SAGE PR gambit: Re-create as a pip package pygambit (help wanted!) sagemath/sage#37809