FIX (game_theory): fix polym_lcp_solver type hints in howson_lcp

[mnshkw]

Summary

This PR fixes the return type annotation of polym_lcp_solver in quantecon.game_theory.howson_lcp so that it matches the function’s actual return values.

This is a typing-only change.

Motivation

polym_lcp_solver returns:

• NE (a tuple of per-player mixed strategies) when full_output=False
• (NE, NashResult) when full_output=True

The previous type hint did not accurately represent the full_output=True case.

Changes

• Update the return type annotation to reflect:
  • NE as tuple[NDArray, ...]
  • the full_output=True case as a 2-tuple (NE, NashResult)

Notes for Reviewers

All codes and documentation are written with assistance by LLMs.

[coveralls]

coverage: 92.586%. remained the same
when pulling e0d5c39 on mnshkw:fix/howson-lcp-type-hints
into 92cb823 on QuantEcon:main.

[oyamad]

@mnshkw Thanks! I added a commit that corrects the description in the Returns section.

@mmcky This is ready to merge. Thanks.

[mmcky]

thanks @mnshkw and @oyamad -- once I get the green ticks I will merge this.

[Copilot]

Pull request overview

This PR updates the type annotation for polym_lcp_solver in quantecon.game_theory.howson_lcp so static typing matches the function’s two return modes (full_output=False vs True) in the game theory solvers.

Changes:

• Fix polym_lcp_solver return type hint to represent NE vs (NE, NashResult) accurately.
• Adjust the docstring “Returns” section to better reflect the intended outputs.