===============
CoalitionalGame
===============

Constructor
------------
Creating a CoalitionalGame object takes a dictionary where the key is a tuple (or frozenset) whose members
are the members of a coalition and whose values are the values of that coalition. Additionally there is an
optional boolean value isCost (default False) indicating this is a cost game.
The constructor will "fill in" dictionary values not given according to the rule that the value of a coalition
is the highest value of any subcoaltions where there is an explicit value.
The empty coalition is assumed to have value zero.

    from coalitions.coalitionalgame import CoalitionalGame
    vals = {('L1', 'R'):1,('L2', 'R'):1}
    cgg =  CoalitionalGame(vals)

Methods
---------

get_is_core(self, imputation)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Return a boolean indicating whether the passed in imputation is part of the core. Because of the perils of
checking floating point equlities, this method may return the wrong answer. This module comes with no guarentees in
any case. 

get_is_additive(self)
~~~~~~~~~~~~~~~~~~~~~~
Returns a boolean.


get_is_simple(self)
~~~~~~~~~~~~~~~~~~~~
Returns a boolean


get_banzhaf_values(self)
~~~~~~~~~~~~~~~~~~~~~~~~~~
Returns a dict where the key is the player label and the value is the Banzhaf value.


get_shapley_values(self)
~~~~~~~~~~~~~~~~~~~~~~~~~
Returns a dict where the key is the player label and the value is the Shapley value.

simulate_shapley_values(self, perms)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For large player sets it may not be feasible to calculate the Shapley values precisely, since this requires
checking the values of all subcoalitions. This method calculates an approximate Shapley value using a fixed number
of permutations.
Returns a dict where the key is th player label and the value is the Shapley value.

zero_normalize(self)
~~~~~~~~~~~~~~~~~~~~~
return a pair theGame, newgrand where game is the zero-mormalized new game and newgrand is the value of the
grand coalition in the new game ( 1, 0 or -1).


is_equivaluent(self, game):
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check whether the the passed game is stratgeically equivalent to this game. returns a boolean.

get_is_monotonic(self)
~~~~~~~~~~~~~~~~~~~~~~~~
returns a boolean

get_is_superadditive(self)
~~~~~~~~~~~~~~~~~~~~~~~~~~
Returns a boolean



create_voting_game(player_strengths, crit)
-------------------------------------------

This consruction method takes a dictionary with key player_type and value voting strength, plus the critival value
form the vote to carry. So long as the sums of the voting strengths of the players of a coalition is 
greater than or equal to the critical value, the coalition value is 1. Otherwise it is zero.