clay-borg/research/CB-RES-0009-extensive-form-is-the-lingua-franca.md

---
id: CB-RES-0009
capability: analysis.gametheory
status: draft — survey only, no decision taken
tier: M
chaos: not rolled — this is a survey, not a pass that changes the loop
---

# CB-RES-0009 — extensive form is the lingua franca

Surveyed 2026-08-08. Answers two questions put by the maintainer:
**is there a good game-theory mapping to Ludii's game description
language**, and **is that language formal enough to derive one from?**

**Short answers: yes, and no — but the second does not matter, because
the first already gives us the object we want.**

---

## 1. The mapping exists, and it is the extensive-form game

*The Ludii Game Description Language is Universal* proves that Ludii's
language **can represent an equivalent game for any arbitrary finite,
non-deterministic, imperfect-information game**, extending earlier work
that covered only *"finite, deterministic, fully observable extensive-form
games"*. The paper is explicitly grounded in **extensive-form games**.

So the mapping is not something to invent. **It is the theorem.**

An extensive-form game (EFG) is the standard game-theoretic object:

| EFG component | what it is |
|---|---|
| **histories** | sequences of actions from the root |
| **information sets** | histories a player cannot tell apart — where imperfect information lives |
| **chance nodes** | nature's moves, with probabilities |
| **payoffs** | utilities at terminal histories |

**Simultaneous moves are already covered**: the standard EFG encoding
sequences them and hides the earlier move in an information set. GROUND's
commit/reveal *is* that encoding.

## 2. And it is the same object OpenSpiel uses

This is the part that makes it useful rather than merely true.

[OpenSpiel](../simulators/openspiel.md)'s API is an EFG interface, and
its algorithms — CFR, best-response, **exploitability** — operate on EFG
structure. It states support for simultaneous-move,
imperfect-information and cooperative games, which is all four of
GROUND's awkward properties.

> **Ludii → EFG ← OpenSpiel.** The extensive-form game is the interchange
> format between "describing a game" and "analysing it", and both
> neighbours already speak it.

## 3. Is Ludii's language formal? Syntax yes, semantics no

This is the sharp part of the answer.

**The syntax is formal, and unusually so.** Ludii uses a **class grammar**:
the grammar is *automatically derived from the source code*, so keywords
(ludemes) and their permitted argument types come from the class
hierarchy. A game is a quintuple of ludemes — Name, Players, Mode,
Equipment, Rules.

**The semantics are the implementation.** In the surveyed material's own
words, *"Ludii effectively makes its programming language (Java) the game
description language, and as a result, it can theoretically support any
rule, equipment or behaviour that can be programmed in Java."* A ludeme
means what its Java class does. Compilation yields a forward model —
legal moves, apply, copy.

So:

> **There is no independent mathematical semantics to extract.** The
> formality lives in the *universality result*, which is a statement about
> what the language can express, not in a calculus defining what a
> description means.

**Contrast with GDL**, which has a genuine logical semantics defined
independently of any interpreter — and pays for it in verbosity and
speed: Ludii is measured as **six times faster** on Gomoku 15×15, twenty
on Amazons and Hex, and **over two hundred** on Chess.

**That is the real trade, and it is not "Ludii vs GDL". It is:**

| you can have | you give up |
|---|---|
| semantics defined independently (GDL) | speed, concision, readability |
| speed and a machine-derived grammar (Ludii) | a definition of meaning that survives the implementation |

## 4. The conclusion for clay-borg

**Do not derive a description language from Ludii.** There is nothing
semantic to derive, and copying its approach would make *our* Rust the
definition of meaning — which is what we already have, unlabelled.

**Target the EFG directly.** It is the formal object, the universality
proof says it is expressive enough for anything we will model, and it is
what buys the game theory.

### 4.1 We are closer than the tracks assumed

clay-borg already has most of an EFG, under other names:

| EFG component | what we already have |
|---|---|
| histories | the **journal** — `Applied { actor, command, events }` in order |
| legal actions | `bot::legal_commands(state, seat)` |
| **information sets** | **`state.project(Viewer::Player(seat))`** — the projection *is* the information partition |
| payoffs | `Outcome` / `score()` |
| terminal | `outcome.is_some()` |

**The projection is the find.** `Project`/`Viewer` was built so a player
is not shown another's hand ([INTENT](../INTENT.md) decision 7). It is,
unremarked, the machinery an EFG needs for imperfect information.

### 4.2 Three gaps, and one of them is checkable today

**Chance is folded, not explicit.** `setup` shuffles the deck, deals, and
draws the Lead from a seeded RNG; the mid-game reshuffle derives from seed
and round. So **a clay-borg game is one chance realisation, not a game
with chance nodes** — and our panels approximate the chance distribution
by sampling seeds. That is legitimate Monte Carlo, and it is *not* an EFG
with a chance player. CFR needs the latter.

**Perfect recall is unasserted.** CFR and exploitability assume **perfect
recall**: a player remembers their own past actions and observations.
Whether our per-seat projection sequence satisfies it is **a property of
this engine that nobody has checked**, and it is checkable —
reconstruct each seat's observation sequence from the journal and require
that no two histories in one information set disagree about that seat's
own past.

> **This is the concrete next step for Track B**, and it is small. If
> perfect recall fails, every equilibrium concept we might quote is
> unsound here, and that is worth knowing before adopting anything.

**Simultaneity is encoded but not stated.** Commit/reveal is the textbook
EFG encoding of simultaneous moves. Saying so costs nothing and removes a
question a reviewer would otherwise have to ask.

## 5. What this does to the tracks

- **Track A**: the description-language question narrows. The choice is
  not "our language or Ludii's" but **"what is the cheapest thing that
  emits an EFG"** — and Ludii is then a possible *front end*, not a rival.
- **Track B**: was "build a game-theory agent". It is now **close the
  three gaps in §4.2, then adopt**. The first task is a checkable
  property, not a design.

## 6. What was not checked

- **The universality paper's proof itself** — only its abstract and
  framing were read. The theorem statement is quoted second-hand.
- **Whether OpenSpiel's exploitability is meaningful for a co-operative
  game with a shared threshold.** Still open, still the question that
  decides whether Track B adopts or only borrows vocabulary.
- **Ludii's licence**, and whether a front-end use is permitted.
- Whether Ludii can express a **binding multi-round state machine** like
  DARVO concisely. Universality says it *can* be expressed; it says
  nothing about whether the description stays readable, which is Ludii's
  actual selling point.

## Sources

- *The Ludii Game Description Language is Universal*
  (https://arxiv.org/abs/2205.00451)
- *An Overview of the Ludii General Game System*
  (https://arxiv.org/pdf/1907.00240) and *Ludii Game Logic Guide*
  — for the class grammar and Java-as-semantics point
- *Game Description Languages: the Good, the Bad, and the Ugly*, Björnsson
  (https://ludii.games/TalksWorkshop/Bjornsson.pdf)
- OpenSpiel (https://github.com/google-deepmind/open_spiel)
- *A note on the empirical comparison of RBG and Ludii*
  (https://arxiv.org/pdf/1910.00309) — the speed figures