Neural Equilibrium Solvers for OpenSpiel

[alexunderch]

This PR attempts to introduce the concept of Neural equilibrium solvers, following the papers:

1. Turbocharging Solution Concepts: Solving NEs, CEs and CCEs with Neural Equilibrium Solvers (arXiv:2210.09257)
2. Deep Incentive Design with Differentiable Equilibrium Blocks (arXiv:2603.07705)

So far, we've got [Ready for the review]:

1. Sampling utility for OpenSpiel and Random games (L-invariant) based on the paper [1]
2. Implementations of the equivariant architecture
3. Evaluation metrics
4. NES Module
5. Test coverage of all the above

In the draft stage:

1. Mechanism design modules and losses

This pull request in created maybe too early to facilitate the development process (Dr. Marris may or may not be somewhat shy). I think that it does not currently learn correctly (from the fundamental perspective) and lacks some utility (see README).

CC to @lanctot : for a while, don't run the CI/CD: it takes some time and I haven't put the tests to the Makefile, until we fix we ensure that I match that "internal" implementation in necessary capacity. Thank you.

@lukemarris, your turn.

P.s. I understand that I did use AI to fulfill some code snippets in question. However, whole code was read and run by me, and I'll eliminate these parts in the future: I had no1 to ask questions, sorry.

[lanctot]

Can you add NES to docs/algorithms.md?

[lanctot]

Thanks!

[lukemarris]

First pass through.

I would focus on:

• Just CCE
• Just ME
• Fixed shape game (say 4x4) No masking

When that is working well we can add the other bells and whistles.

[lanctot]

Changes look good on my side but would still like Luke's final OK before we import. Let's continue this when he's back