1.A writes his salary = A + random number

2.A asks B to add a particular number to his salary and send it to C.(C is not told what the number is).
B writes his salary + random2.

3. A asks C(B does not know this) to subtract from the total, (random number)+(random2). C then gets the correct sum and finds the average.

It seems like no scheme is liar proof and immune from all-but one collusion. I suspect these are reasons much salary information is obtained anonymously or from a single trusted source rather than through a voluntary exchange among people who don’t trust each other.

The problem is once again, if any player was going to lie (which is essentially what the colluding players are doing, since the terms were that each player provide their salary; something a colluding player is now refusing to do i.e. the refusal can be mathematically considered either null, or a “made up salary” with no value) and collude in the first place, then there are no solutions for this game. Even with the standard solution, there’s no way to go around this problem.

I re-iterate, the point of this solution isn’t doing what the standard solution cannot address, it’s just a simpler way of accomplishing the same tasks, given certain conditions. The most important condition in this question is that players do not lie. If they don’t lie, they will not collude either. If they do lie, then there are no solutions, since they will all be inclined to lie, and no one gives out their real salary.