Hello sage-devel,

I am a Google Summer of Code 2026 applicant applying to the Gambit project. 
One of my project tasks is to complete and update the SageMath PR #37809 
(https://github.com/sagemath/sage/pull/37809), which integrates pygambit 
(the Python package for Gambit 16.x) with SageMath.

I have studied the PR and the current pygambit 16.5.0 API carefully. The 
main issue is that ExternalLCPSolver and ExternalLPSolver no longer exist 
in pygambit — the correct replacements are gbt.nash.lcp_solve() and 
gbt.nash.lp_solve(), which return NashComputationResult object.

Before I begin working on the code, I have a few questions:

~Should I rebase mkoeppe's branch (gambit_repair) or open a fresh PR on 
sagemath:develop?
~Is there a preference on whether pygambit should be standard vs. optional 
in SageMath's package system?
~Are there any other changes in SageMath's game_theory module since April 
2024 that I should be aware of?
Thank you
 Sumit Goyal

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