Collusion between bidders can lead to a loss in revenue, and is a significant concern in practical auction design. Assume that potential colluders know each others values.

1. Consider an SPSB auction. Suppose bidders with values $4, $8 and $10 collude, while a fourth bidders bid is fixed at $6. How can bidders 1, 2 and 3 bid in order to collude, how might their proceeds be divided to keep all members of the coalition happy, and why can bidders 1 and 2 not usefully deviate from this play? You do not need to provide a formal equilibrium analysis.