tegwick
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Two questions from the maintainer — is there a game-theory mapping to Ludii's language, and is that language formal enough to derive one from. Yes, no, and the no does not matter. The mapping is proven, not to be invented: "The Ludii Game Description Language is Universal" shows the language can represent an equivalent game for any finite, non-deterministic, imperfect-information game, extending earlier work limited to finite deterministic fully-observable extensive-form games. EFG is also OpenSpiel's object, so the same formalism connects description to analysis: Ludii -> EFG <- OpenSpiel. Ludii's syntax is formal and unusually so — a class grammar derived automatically from its source. Its semantics are its Java: a ludeme means what its class does, and Ludii effectively makes Java the game description language. So there is no independent calculus to extract. The formality lives in the universality RESULT, not in a definition of meaning. GDL has the semantics and pays for it in speed — six times on Gomoku, twenty on Amazons and Hex, over two hundred on Chess. Conclusion: do not derive a language from Ludii; target the EFG directly. And we are closer than the tracks assumed. The journal is the history, Outcome is the payoff, legal_commands gives the actions — and project(Viewer::Player(seat)) IS the information partition, built so a player is not shown another's hand and unremarked as exactly the machinery imperfect information needs. Three gaps: chance is folded into a seed so a game is one realisation rather than a game with chance nodes; perfect recall is unasserted, which CFR and exploitability both assume; and commit/reveal is the standard EFG encoding of simultaneity but is never stated as such. Perfect recall is checkable from the journal today and is now Track B's first task — if it fails, every equilibrium concept we might quote is unsound here. Also re-vendored the catalog twice: ground-game added H2 — scoped problem stress, applying End Stress by personal/bond/global scope instead of flat to everyone, which is a direct response to our reading that H1's tax scales with the Problems while its intended effect does not. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> |
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