Normalise payoffs in vertex enumeration

[choosen23]

Two commits: the first unbreaks CI on current tooling, the second is the actual fix. Details on the
first are at the bottom.

The problem

vertex_enumeration returns an empty generator — no exception, no warning — for games it solves
correctly when the payoffs are smaller.

import numpy as np
import nashpy

for name, A, B in [
    ("RPS", [[0, -1, 1], [1, 0, -1], [-1, 1, 0]], [[0, 1, -1], [-1, 0, 1], [1, -1, 0]]),
    ("BoS", [[3, 0], [0, 2]], [[2, 0], [0, 3]]),
]:
    for k in (0, 3, 6, 9, 12):
        game = nashpy.Game(np.array(A, dtype=float) * 10**k, np.array(B, dtype=float) * 10**k)
        print(name, f"x1e{k}", "->", len(list(game.vertex_enumeration())), "equilibria")

equilibria found	×1e0	×1e3	×1e6	×1e9	×1e12
RPS	1	1	1	0	0
Battle of the Sexes	3	3	3	0	0

This is not degeneracy

Flagging this up front, since #39 and #66 were both reports of empty results that turned out to be
degeneracy. This one isn't:

• Rock-Paper-Scissors and Battle of the Sexes are both non-degenerate.
• Both are solved correctly at ×1e6.
• The only change between the working and failing rows is multiplying every payoff by a constant.

Degeneracy is invariant under a positive rescaling of payoffs, so it cannot explain a failure that
appears only at ×1e9. And since every finite game has at least one equilibrium, an empty return is
never a correct answer here.

Root cause

The best response polytope is {x >= 0, Mx <= 1}. Because the right hand side is fixed at 1, the
vertex coordinates scale as 1 / payoff. non_trivial_vertices discards the origin with

if not np.all(np.isclose(v, 0)) and max(v) < np.inf

and np.isclose(v, 0) reduces to its absolute tolerance atol=1e-8 when comparing against zero. So
once payoffs are large enough, every legitimate vertex falls under atol and is thrown away as the
trivial vertex:

payoffs x1e0 : raw vertex max|coord| = 5.00e-01 -> 3 kept
payoffs x1e6 : raw vertex max|coord| = 5.00e-07 -> 3 kept
payoffs x1e9 : raw vertex max|coord| = 5.00e-10 -> 0 kept

The fix

Normalise in vertex_enumeration, just after the existing shift to non-negative payoffs. Nash
equilibria are invariant under a positive rescaling of each player's payoffs, so this does not change
the result — it just keeps the polytope well conditioned so the existing tolerance is meaningful.

I first tried the smaller change, making the zero test in polytope.py scale-relative, and it is
not a good fix: it lets through vertices whose labels are then computed incorrectly, returning 49
spurious "equilibria" with a normalised regret of 1.0 at ×1e9, and crashing in find_feasible_point
at ×1e15. Fixing the conditioning at the source avoids that.

Test plan

• New regression test test_with_large_utilities, checking all three equilibria of Battle of the
  Sexes at scales 1, 1e6, 1e9 and 1e12. It fails on main with 0 = len([]) and passes here.
• Verified independently in exact rational arithmetic: with the fix, every returned profile has a
  normalised regret at float precision (2.8e-17 or lower) for scales up to ×1e18.

Full tox command set locally:

black --check src/ tests/	clean
mypy --ignore-missing-imports src/nashpy	Success, no issues in 25 files
interrogate --fail-under 100	100%
pytest . --cov=nashpy --cov-fail-under=100 + doctests	225 passed, 100% coverage
flake8 src/ tests/	clean

The first commit: unbreaking CI

Two tox commands fail on main under current tooling releases, and both run before the tests, so CI
is currently red on every open pull request:

• black --check src/ — recent black releases collapse these short .format calls onto a single
  line (game.py, support_enumeration.py).
• mypy — imitation_dynamics is annotated Generator[Tuple[float, float], Any, None] but yields a
  pair of arrays. Corrected to Tuple[npt.NDArray, npt.NDArray].

Formatting and one annotation, no behaviour change. Kept as a separate first commit so it can be
dropped or cherry-picked independently if you would rather handle it another way.

[choosen23]

A note on the red CI here: the run fails at the first tox command, black --check src/, on game.py and support_enumeration.py — neither of which this branch touches. It never reaches the tests.

Both of those, plus a mypy error in imitation_dynamics.py, are pre-existing on main under current tooling releases, so CI is red for every open pull request right now. I have put the fix for that in #245, which is formatting and one type annotation only.

Once #245 is in I will rebase this branch and CI should be green. Happy to reorder or combine them if you would rather.