Add 3 player max cut test for enumpoly solver

[ameliekleber]

This PR adds a test for the enumpoly solver that covers the 2x2x2 max cut normal form game, ensuring it returns the two pure and one mixed equilibirum.

[ameliekleber]

@rahulsavani I added the test we discussed on Wednesday, would appreciate your review :)

[Copilot]

Pull request overview

Adds a targeted regression test to ensure enumpoly_solve correctly finds all equilibria (two pure + one symmetric mixed) for a 3-player 2x2x2 max-cut-derived normal-form game.

Changes:

• Adds a new ENUMPOLY_STRATEGY_CASES test case validating three equilibria for a 2x2x2 NFG.
• Updates the .nfg test game’s header comments to document the mixed equilibrium structure.
• Registers a new pytest marker (nash_enumpoly_strategy) and wires the new case into the main strategy-solver parametrization.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 1 comment.

File	Description
tests/test_nash.py	Adds and registers an enumpoly strategy-form equilibrium test case for a 3-player 2x2x2 NFG.
tests/test_games/2x2x2_nfg_from_local_max_cut_2_pure_1_mixed_eq.nfg	Clarifies documentation for the symmetric mixed equilibrium in the test fixture.
pyproject.toml	Adds the nash_enumpoly_strategy marker so --strict-markers remains satisfied.

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[rahulsavani]

Thanks, this looks good to me, though co-pilot is right, we should probably include a regret_tol too. This max cut game is super simple so it may never error, but it's still good practice. For the suggestion below with nau2004, we'll definitely need that anyway.

Further suggestion:

Sorry to be demanding but I didn't realise we had no tests at all for "ENUMPOLY_STRATEGY", could you perhaps add a couple more, e.g. a 2-player coordination games would be natural (say in dimension 4 where we expect 7 eq, assuming it runs quickly enough, or dim 3 if not), for one or two further 3-player games you could try:

gbt.catalog.load("journals/ijgt/nau2004/sec4")
gbt.catalog.load("journals/ijgt/nau2004/sec5")

If sec5 takes too long for stop_after=None, feel free to set it otherwise.

Thanks.

[tturocy]

@rahulsavani Further to our in-person conversation, indeed it looks like we never got around to doing strategy versions of tests for enumpoly - likely due to combination of issues with coordination games and with ordering of outputs...!

[ameliekleber]

I've added the 3 test you requested, the two from the catalog and the coordination game for n=3 (I think this is what you meant as this one has 7 eq and n=4 has 15?). The coordination game test was already in the behavior tests for enumpoly, so I added the use_strategic parameter for this test

[rahulsavani]

I've added the 3 test you requested, the two from the catalog and the coordination game for n=3 (I think this is what you meant as this one has 7 eq and n=4 has 15?). The coordination game test was already in the behavior tests for enumpoly, so I added the use_strategic parameter for this test

You are right I have an "off by one error" with my reference to the dimensions of the coordination game: n=3 is good.

[rahulsavani]

https://github.com/all-contributors

please add @ameliekleber for code

[rahulsavani]

@tturocy

    # A three-player 2x2x2 game with 3 pure, 2 incompletely mixed, and a continuum of completely mixed Nash equilibria (nau2004 sec5 catalog game)
    pytest.param(
        EquilibriumTestCase(
            factory=functools.partial(gbt.catalog.load, "journals/ijgt/nau2004/sec5"),
            solver=functools.partial(gbt.nash.enumpoly_solve, stop_after=None),
            expected=[
                    [d(1, 0), d(0, 1), d(1, 0)],
                    [d(0, 1), d(1, 0), d(1, 0)],
                    [d(0, 1), d(0, 1), d(0, 1)],
            ],
            prob_tol=TOL,
            regret_tol=TOL,
        ),
        marks=pytest.mark.nash_enumpoly_strategy,
        id="test_enumpoly_strategy_4",

This is more like a regression test because I am not sure that we should only get the pure here -- or is this clear to you?

[rahulsavani]

Looks good.

One minor thing is flake8 -- please install pre-commit, which will help with this.

For a quick look at the required changes in this case, please see what co-pilot did in PR #972