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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
180 lines
6.8 KiB
Markdown
180 lines
6.8 KiB
Markdown
---
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id: CB-WP-0041
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kind: product
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title: "The extensive-form foundation"
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status: active
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state_hub_workstream_id: "dacfa1fe-81c3-4c97-b81e-ec66d95a611c"
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---
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# Purpose
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```
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structural tier M (states what the kernel claims about itself as a
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game-theoretic object, and prepares — but does not
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build — a capability port)
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chaos d8 = 5 → no override
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declared tier M
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```
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**Declaration 1 of chaos window 4.** Window 3 closed at 12 declarations
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with one override that changed nothing, and **its verdict is still owed**
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([`ChaosRollHistory.md`](../specs/ChaosRollHistory.md)).
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## Why
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[CB-RES-0009](../research/CB-RES-0009-extensive-form-is-the-lingua-franca.md)
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found that the **extensive-form game is the interchange format** between
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describing a game and analysing it — Ludii's universality result grounds
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its language in EFGs, and OpenSpiel's CFR, best-response and
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exploitability consume them.
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**And that we already have most of one**, under other names:
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| EFG component | ours |
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|---|---|
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| histories | the journal — `Applied { actor, command, events }` in order |
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| actions | `bot::legal_commands(state, seat)` |
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| **information sets** | **`state.project(Viewer::Player(seat))`** |
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| payoffs | `Outcome` / `score()` |
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| terminal | `outcome.is_some()` |
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**This workplan does not build the port.** It answers what is true of the
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engine today, because a port built on an unchecked assumption is worse
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than no port — and one of the three gaps invalidates every equilibrium
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concept if it turns out badly.
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## Task: does the engine satisfy perfect recall?
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```task
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id: CB-WP-0041-T01
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status: done
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priority: high
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state_hub_task_id: "a9438152-1556-4cde-9eae-af75066a485a"
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```
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**Perfect recall** — every player remembers their own past actions and
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observations — is the assumption **CFR and exploitability both rest on**.
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Nobody has checked whether ours holds.
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Formally, for a seat `i` and any two histories `h`, `h'` in the same
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information set of `i`: the *sequence of `i`'s own actions and
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information sets* along `h` and `h'` must be identical.
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**Controls:**
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- **derived from the journal and the projection**, not asserted — the
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check must be able to say NO;
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- **a positive control**: a deliberately forgetful projection must fail
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it, or the check proves nothing;
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- **stated per seat count**, since the partition depends on how many
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seats there are to hide from;
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- **the answer may be that we do NOT have perfect recall**, and that is
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reported as plainly as the other outcome. It would be a real finding
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and would make Track B's adoption unsound as it stands.
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**Done 2026-08-08. The answer is "it depends what you call an information
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set", and the distinction is the result.** 44,938 decision points, random
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play, 2/3/4/6 seats.
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| reading | information set is… | violations |
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|---|---|---|
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| **A** | the seat's **current projection** — what `project(Viewer::Player(seat))` returns and the page renders | **22** |
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| **B** | the seat's **observation history** — every view seen and action taken, in order | **0** |
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**Reading A fails, and the witness is concrete**: two histories reach a
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byte-identical view — round 3, Select, same hand, same claimed Problem —
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where the seat had played `SOLVE, GROUND—OU(protect)` in one and
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`SUPPORT, SOLVE` in the other. **The view does not tell the seat what it
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did.**
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**The mechanism is that our state is a snapshot, not a history.**
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Selections clear each round and effects coincide, so a player cannot
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reconstruct their own past from the present. In a real game the player's
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memory supplies it; in the state, nothing does.
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**This is precisely OpenSpiel's `ObservationString` vs
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`InformationStateString` split**, arrived at here by measurement rather
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than by reading it off. `project()` is an *observation*.
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**So Track B is not closed — it is constrained**, and usefully:
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> **An extensive-form game built from this engine must key information
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> sets on observation histories, never on `project()`.**
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**Both directions are asserted.** Reading B empty, *and* Reading A
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non-empty — because if the sample stops finding Reading A violations the
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conclusion is unsupported and must be re-derived, not quietly kept.
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**What this cannot say.** It samples; it can falsify perfect recall and
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cannot establish it. Reading B's zero means *no counterexample was
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drawn*, which is weaker than "the property holds" and is printed as such.
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## Task: say precisely what our chance is
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```task
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id: CB-WP-0041-T02
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status: todo
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priority: high
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state_hub_task_id: "e223bf7d-6e4e-4377-8eac-a63e83a60d35"
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```
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`setup` shuffles, deals and draws Lead from a seeded RNG, and the
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mid-game reshuffle derives from seed and round. **So a clay-borg game is
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one chance realisation, not a game with chance nodes**, and the panels
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approximate the distribution by sampling seeds.
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**Controls:**
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- **state it, do not fix it.** Monte Carlo over seeds is legitimate and
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is what we do; the defect would be calling it an EFG;
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- **name every point where chance enters**, from the code, not from
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memory;
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- **say what an explicit chance player would cost** — that is the input to
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T04's decision, and guessing it is how a port gets built on a hope.
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## Task: state the simultaneity encoding, and check it
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```task
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id: CB-WP-0041-T03
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status: todo
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priority: medium
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state_hub_task_id: "c95b32a1-5006-4acd-abc9-537543119344"
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```
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Commit/reveal **is** the textbook EFG encoding of simultaneous moves:
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sequence them, and hide the earlier move in an information set.
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**Control:** it is not enough to say so. **The projection must actually
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hide another seat's selection before Reveal**, and a test must fail if it
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stops doing that. That property is load-bearing for every claim in §1 of
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the research note and is currently only implied by
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`SelectionView::Hidden`.
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## Task: decide whether to build the port at all
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```task
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id: CB-WP-0041-T04
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status: todo
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priority: medium
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state_hub_task_id: "3010fb0d-84cc-4fa8-8c23-726ee946cd79"
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```
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`decisions/ADR-*.md`, written **after** T01–T03 and not before.
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**It must be able to conclude "no".** Options include exporting an EFG,
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adopting OpenSpiel's API directly for analysis only, or deciding the gaps
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are too expensive and Track B borrows vocabulary rather than machinery.
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**Controls:**
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- **the decision cites T01's answer**, because if perfect recall fails,
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most of the option space closes;
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- **it states what it would cost to be wrong**;
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- **a port is declared separately, at its own tier.** Creating a capability
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port is a tier-L trigger and this workplan is M — it may not smuggle one
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in.
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## Not in this workplan
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- **No EFG export, no OpenSpiel integration, no equilibrium computation.**
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- **No answer to "is exploitability meaningful for a co-operative game
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with a shared threshold"** — that is the other open question from
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CB-RES-0009 §6, it is a question about game theory rather than about our
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engine, and it wants its own pass.
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