fix: Enforce Subgame Perfection in Sequence Form LP (#1304)

[SH20RAJ]

Description

Enforces subgame perfection in the Sequence Form LP solver, addressing Issue #1304.
Previously, the solver could produce arbitrary policies (e.g., uniform random) in unreachable information states. This PR modifies the formulation to use dual variables (slacks) to extract game-theoretically optimal actions even in unreachable subgames.

Changes

• Modified open_spiel/python/algorithms/sequence_form_lp.py to use slack variables for policy extraction.
• Added check_subgame_perfection.py to verify the fix on Kuhn Poker (asserts Player 0 folds 'J' in unreachable subgame).

Verification

• New Test: check_subgame_perfection.py passes (Output verified locally: "Assertion logic passed: P0 folds correctly.")
• Regression: open_spiel/python/algorithms/sequence_form_lp_test.py passed (6/6 tests).
• Supersedes Implement subgame perfection in Sequence Form LP solver (#1304) #1417 (which was closed due to test environment issues).

Dependencies

Requires cvxopt (and numpy).

[SH20RAJ]

Hi @lanctot and the OpenSpiel team,

This PR serves as a core technical contribution for my GSoC 2025 candidacy. It addresses the subgame perfection issue in the Sequence Form LP solver (Issue #1304), which is critical for equilibrium finding in zero-sum games.

Summary for GSoC Context

• Problem: The LP solver previously produced arbitrary policies in unreachable states, violating subgame perfection.
• Solution: I implemented the use of dual (slack) variables to correctly infer optimal actions even when the realization probability is zero.
• Validation:
  • Reproduced the original failure from PR Implement subgame perfection in Sequence Form LP solver (#1304) #1417.
  • Fixed the environmental/dependency issues (numpy/cvxopt import errors).
  • Added check_subgame_perfection.py which formally asserts that Player 0 folds a Jack in Kuhn Poker even in the unreachable subgame (the classic test case).
  • Verified that all existing regression tests in sequence_form_lp_test.py pass.

I hope this demonstrates my ability to work with the core solver algorithms and ensure mathematical correctness in the codebase. I would appreciate any feedback!

[SH20RAJ]

For completeness regarding my GSoC application, I would also like to cross-reference my other contributions to OpenSpiel:

Merged / Internally Imported:

• PR refactor(algorithms): add type hints to cfr.py #1412: refactor(algorithms): add type hints to cfr.py
• PR refactor(examples): add type hints to tic_tac_toe_qlearner #1411: refactor(algorithms): add type hints to external_sampling_mccfr.py

Active / Ready for Review:

• PR feat: Implement Serialize for MCTSBot (#1257) #1466: MCTS Serialization (Essential for checkpointing/experiments).
• PR feat: GSoC 2025 Contributions - Core Updates & Optimizations #1454: Core Updates (Includes optimizations for Euchre/UniversalPoker and standardized Kuhn/PhantomTTT fixes).

This set of PRs covers core algorithms, game logic correctness, infrastructure/serialization, and code quality (typing).

[SH20RAJ]

Hi @lanctot and maintainers, checking in on this subgame-perfection fix for #1304 as part of my GSoC 2026 prep. If there's a preferred narrower scope, extra validation, or anything I should revise to make review easier, I'm happy to update it. Thanks for taking another look when you have time.

[lanctot]

Hi @SH20RAJ ,

I was waiting for the tests to pass before taking a look. Now that I see this more closely, I think #1489 subsumed it, so we should probably close this.

If you would like to make a contribution to OpenSpiel, I think it'd be best to discuss what it could be before you go off to implement something based on the issues. Feel free to open an issue yourself to discuss, or comment on an open issue to ask the status.

[lanctot]

I've now put up a post for new contributors: #1511

This would have been an example where I would likely have discouraged a PR because the conversation in that issue was a bit confusing. The initial suggestion did not make much sense to me. I think sequential equilibrium made more sense, and it was added in #1489 .

Happy to discuss future contributions, but let's try to talk about what they could be first (by responding to or opening a new issue). Thanks.