Abstract
Collusion here takes the form of a side transfer between two bidders proposed by a mediator, before a first-price auction with independent private values. I find a necessary and sufficient condition, in terms of the bidders’ prior distributions, for existence of a side transfer acceptable to all types of both bidders on path of a perfect Bayesian equilibrium. The class of distributions defined by this condition is larger than the class under the passive updating assumption in the mechanism design literature on collusion. The off-path posterior belief most conducive to collusion entails a continuation equilibrium as if the collusion vetoer were bidding against a naive, value-bidding rival.
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