Shapley value (fast)

Calculates Shapley value

Any suggestions will be appreciated!
Speed (Intel Core i7, 2.2 GHz, 8 GM RAM, 64-bit)
n = 2: 0.433 ms
n = 3: 0.439 ms
n = 4: 0.542 ms
n = 5: 0.671 ms
n = 6: 0.810 ms
n = 7: 1.032 ms
n = 8: 1.306 ms
Inputs:
v:
(1, 2^n-1)
worth of each coalition
(expected sum of payoffs for the members in a coalition)
originalcoalitions:
(2^n-1, n)
OPTIONAL
if coalitions are not following the order of binary
numbers (see example below)
firstplayer:
string
OPTIONAL
'left' / 'right' (default)
'left', if the first player is denoted by
[1, 0, 0, ..., 0] in originalcoalitions, and right,
if it is denoted by [0, ... 0, 0, 1]
Output:
vector of n elements [value for player_1, player_2,..., player_n]

CONSTRUCTING THE INPUT VECTOR
Binary numbers represent the coalitions.
For example, for n = 3 players,
binary numbers from 1 to 2^n-1: [001, 010, 011, 100, 101, 110, 111]
Coalitions: {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}
So v = [payoff for {1}, payoff for {2}, payoff for {1, 2}, payoff for {3},...]

[player_3, player_2, player_1]
c = [0, 0, 1;
0, 1, 0;
0, 1, 1;
1, 0, 0;
1, 0, 1;
1, 1, 0;
1, 1, 1];
v = [0, 0, 0, 0, 1, 1, 1];
shapley(v)
shapley(v, c, 'right')

In case coalitions are ordered differently:
[player_3, player_2, player_1]
c = [1, 1, 1;
0, 1, 0;
1, 0, 0;
0, 1, 1;
1, 0, 1;
1, 1, 0;
0, 0, 1];
v = [1, 0, 0, 0, 1, 1, 0];
shapley(v, c)
shapley(v, c, 'right')

Suppose that the first player now is on the left hand side:
[player_1, player_2, player_3]
c = [1, 0, 0;
0, 1, 0;
0, 0, 1;
1, 1, 0;
1, 0, 1;
0, 1, 1;
1, 1, 1];
v = [0, 0, 0, 0, 1, 1, 1];
shapley(v, c, 'left')

INTERPRETING RESULTS
The result is a vector containing n elements:
[value for player_1, player_2, player_3] independently of the position of the first player (left/right side) in the coalition matrix