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tucoopy.diagnostics.core_cover_diagnostics

Core cover diagnostics.

This module provides membership-style diagnostics for the core cover (a polytopal superset of the core defined via minimal rights and utopia payoffs).

Examples:

>>> from tucoopy import Game
>>> from tucoopy.diagnostics.core_cover_diagnostics import core_cover_diagnostics
>>> g = Game.from_coalitions(n_players=2, values={0: 0, 1: 0, 2: 0, 3: 1})
>>> d = core_cover_diagnostics(g, [0.5, 0.5])
>>> d.in_set
True

core_cover_diagnostics 

core_cover_diagnostics(
    game, x, *, tol=DEFAULT_GEOMETRY_TOL
)

Membership diagnostics for the core cover.

$\(\text{CoreCover}(v) = \{ x : \sum_{i=1}^n x_i = v(N), m_i \leq x_i \leq M_i \}\)$.

Parameters:

Name Type Description Default
game GameProtocol

TU game.

 required
x list[float]

Allocation vector of length game.n_players.

 required
tol float

Numerical tolerance used for the efficiency check and bound comparisons.

 DEFAULT_GEOMETRY_TOL

Returns:

Type Description
BoxBoundSetDiagnostics

Diagnostics object including the bounds and any bound violations.

Raises:

Type Description
InvalidParameterError

If x does not have length game.n_players.
Notes

The core cover is defined via:

  • utopia payoff M (upper bounds), and
  • minimal rights m (lower bounds),

combined with efficiency.

Examples:

A minimal 3-player example (only the grand coalition has value 1):

>>> from tucoopy import Game
>>> from tucoopy.diagnostics.core_cover_diagnostics import core_cover_diagnostics
>>> g = Game.from_coalitions(n_players=3, values={
...     0:0, 1:0, 2:0, 4:0,
...     3:0, 5:0, 6:0,
...     7:1,
... })
>>> d = core_cover_diagnostics(g, [1/3, 1/3, 1/3])
>>> d.efficient
True
>>> isinstance(d.violations, list)
True