tucoopy

Python package for cooperative game theory (TU) algorithms and for generating animation specs (JSON) consumed by the JS renderer.

Optional speedups:

• pip install "tucoopy[fast]" (uses NumPy for small linear solves in geometry helpers)
• pip install "tucoopy[lp]" (enables LP-based methods like least-core / nucleolus via SciPy)

Optional visualization:

• pip install "tucoopy[viz]" for Matplotlib visualization (2 or 3 players only)

Optional extras (feature -> extra)

Feature	Extra	Notes
LP-backed methods	lp	SciPy backend (recommended)
LP-backed methods (fallback)	lp_alt	PuLP backend
Speedups	fast	NumPy helper routines
Static visualization	viz	Matplotlib (2 or 3 players only)
Dev tools	dev	pytest + mypy + ruff
Docs build	docs	mkdocs + mkdocstrings

Package layout

• tucoopy.base: game/coalition primitives (bitmask-based)
• tucoopy.properties: game properties / recognizers
• tucoopy.games: classic games (glove, weighted voting, airport, bankruptcy, savings, unanimity, apex, ...)
• tucoopy.geometry: geometry for visualization (core vertices, ...)
• tucoopy.solutions: solution concepts (Shapley, Banzhaf, ...)
• tucoopy.power: voting/simple-game power indices
• tucoopy.transforms: transforms/representations (Harsanyi dividends, ...)
• tucoopy.viz: optional visualization with Matplotlib (games with 2 or 3 players only)
• tucoopy.io: JSON + animation spec helpers
• tucoopy.backends: adapters for optional dependencies (LP, NumPy, ...)

Docs (in this repo): see packages/tucoopy-py/docs/en/index.md (EN) and packages/tucoopy-py/docs/pt/index.md (PT). Examples (runnable scripts): see packages/tucoopy-py/examples/README.md.

Install

pip install tucoopy

Optional extras:

• pip install "tucoopy[lp]" for LP-based methods (least-core / nucleolus / modiclus / balancedness) using SciPy (recommended)
• pip install "tucoopy[lp_alt]" for LP-based methods (least-core / nucleolus / modiclus / balancedness) using PuLP (fallback)
• pip install "tucoopy[fast]" for NumPy speedups (kernel / prekernel and helpers)
• pip install "tucoopy[viz]" for Matplotlib visualization (2 or 3 players only)

Quick example (generate an animation spec)

from tucoopy import Game
from tucoopy.solutions import shapley_value
from tucoopy.io.animation_spec import build_animation_spec

game = Game.from_coalitions(
    n_players=3,
    values={
        (): 0.0,
        (0,): 1.0,
        (1,): 1.2,
        (2,): 0.8,
        (0, 1): 2.8,
        (0, 2): 2.2,
        (1, 2): 2.0,
        (0, 1, 2): 4.0,
    },
    player_labels=["P1", "P2", "P3"],
)

phi = shapley_value(game)
spec = build_animation_spec(
    game,
    series_id="shapley",
    allocations=[phi] * 60,
    dt=1 / 30,
    series_description="Shapley value (static).",
    include_analysis=True,
)
print(spec.to_json())

Nucleolus / least-core (LP)

LP-based methods are behind the optional lp extra:

from tucoopy import Game
from tucoopy.geometry.least_core_set import least_core
from tucoopy.solutions import nucleolus

g = Game.from_coalitions(
    n_players=3,
    values={
        (): 0.0,
        (0,): 1.0,
        (1,): 1.2,
        (2,): 0.8,
        (0, 1): 2.8,
        (0, 2): 2.2,
        (1, 2): 2.0,
        (0, 1, 2): 4.0,
    },
)

lc = least_core(g)
nu = nucleolus(g)
print(lc.epsilon, lc.x)
print(nu.levels, nu.x)

Core non-emptiness certificate (LP)

Bondareva–Shapley balancedness check (behind lp):

from tucoopy import Game
from tucoopy.properties.balancedness import balancedness_check

g = Game.from_coalitions(
    n_players=3,
    values={
        (): 0.0,
        (0,): 0.0,
        (1,): 0.0,
        (2,): 0.0,
        (0, 1): 1.0,
        (0, 2): 1.0,
        (1, 2): 1.0,
        (0, 1, 2): 1.0,
    },
)

res = balancedness_check(g)
print(res.core_nonempty, res.objective, res.weights)

Schema (Python <-> JS contract)

• Canonical schema: schema/tucoopy-animation.schema.json
• Bundled schema (package data): packages/tucoopy-py/src/tucoopy/io/schemas/tucoopy-animation.schema.json