How to obtain sum over coalition?

For a given table

1st player 2nd player score

a b 20

b c 10

b d 15

a d 10

I want to get the following results

{a}=0 {b}=0 {c}=0 {d}=0 {a b}=20 {a c}=0 {a d}=10 {b c}=10 {b d}=15 {c d}=0 {a b c}=30 {a b d}=35

{a c d}=10 {b c d} = 25 {a b c d}= 55

Is it possible to obtain above result using matlab code?

Thanks for your comment

Answer 1

[Andrei Bobrov]

s = string(('a':'d')');
ss = s([1 ,2;2,3;2,4;1,4]);
v = [20,10,15,10]';
C = cell(4,1);
for ii = 1:4
    k = num2cell(nchoosek(s,ii),2);
    C{ii} = cell2table(k,'v',{'abcd'});
    C{ii}.value = cellfun(@(x)sum(v(all(ismember(ss,x),2))),k);
end

or

s = string(('a':'d')');
ss = s([1 ,2;2,3;2,4;1,4]);
v = [20,10,15,10]';
C = cell(4,1);
for ii = 1:4
    a = nchoosek(s,ii);
    if ii == 1
        b = a;
    else
        b = join(a,'');
    end
    C{ii} = array2table(b,'v',{'abcd'});
    C{ii}.value = cellfun(@(x)sum(v(all(ismember(ss,x),2))),num2cell(a,2));
end
out = cat(1,C{:});

[HOJUNG LEE]

Thanks for your comment!

BTW, I was trying to apply your code to 3player case with large score column, then I got the message

'ctranspose' is not defined for table

where did I make it wrong?

[Andrei Bobrov]

Please attach small example of your data.

[HOJUNG LEE]

Hello, those are samples of my data.

Thanks for all your comments, it helps me a lot.

a b 19

a b 20

c b 20

b c 21

c b 21

a b 28

b c 28

a b 30

[Andrei Bobrov]

No, attach your data as mat - file.

Answer 2

[Andrei Bobrov]

Variant for your new data from example.mat (B).

BB = B{:,1:2};
abc = unique(BB(:));
n = numel(abc);
C = cell(n,1);
for ii = 1:n
    D = nchoosek(abc,ii);
    a = string(D);
    if ii == 1
        b = a;
    else
        b = join(a,'');
    end
    C{ii} = array2table(b,'v',{'abcd'});
    C{ii}.value = arrayfun(@(x)sum(B.TotalRevenue(...
                              all(ismember(BB,D(x,:)),2))),(1:size(D,1))');
end
out = cat(1,C{:}); 

[HOJUNG LEE]

Thanks for all your help! It nicely works and really helps me a lot!

Answer 3

[HOJUNG LEE]

Here is what I'm working on.