tucoopy.power.holler¶
Holler (Public Good) power index.¶
The Holler index counts how often a player appears in minimal winning coalitions, optionally normalized to sum to one.
holler_index ¶
holler_index(game, *, normalized=True)
Compute the Holler index (also known as the Public Good index) for a simple game.
The Holler index is based exclusively on the minimal winning coalitions of the game. A coalition \(S\) is minimal winning if:
- \(v(S) = 1\), and
- for every \(i \in S\), \(v(S \setminus \{i\}) = 0\).
The Holler index of a player \(i\) is the number of minimal winning coalitions that contain \(i\):
\[ H_i = \#\{ S \text{ minimal winning} \mid i \in S \}. \]
Optionally, this vector can be normalized to sum to 1.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
game | Game | A simple game. | required |
normalized | bool | If True, normalize the index to sum to 1. | True |
Returns:
| Type | Description |
|---|---|
list[float] | Holler index for each player (length |
Notes
- This index focuses only on the essential winning structures of the game, ignoring larger winning coalitions that contain redundant players.
- It is also called the Public Good index because it measures how often a player is indispensable in producing the public good (a winning outcome).
- Unlike Shapley or Banzhaf, this index does not consider coalition sizes or permutations—only the structure of minimal winning coalitions.
Examples:
>>> hi = holler_index(g)
>>> len(hi) == g.n_players
True