Not sure what to call these, which is a part of the problem, as I'd imagine there's plenty of literature on this.
So, consider the following game:
Three players, A, B and C. All of them having finite but sufficient funds.
There is a yes/no decision to be made. Which ever option has the most funds behind it wins. A thinks YES should win and B and C prefer NO. All parties know what the others want. B has a slightly higher utility for getting NO to win (and again all parties know this), and for both this is more important than for A.
A bets \$1000 on YES. Since C knows B needs NO to win, C abstains from contributing to NO side and just let's B to bump the collective offer to \$1001 -> NO wins even without C:s contribution.
Any ideas how to tackle the problem or pointers to literature? The auction can be designed in any way really, but the players will be aware of each others utilities.
Goal is to have a game where the bets from both B and C are in propotion w their utilities of making NO to happen.