Collusive Dominant-Strategy Truthfulness
Fifty years ago, Vickrey published his famous mechanism for auctioning a single good in limited supply. The main property of Vickrey's mechanism is efficiency in dominant strategies. In absence of collusion, this is a wonderful efficiency guarantee. We note, however, that collusion is far from rare in auctions, and if some colluders exist and have some wrong beliefs, then the Vickrey mechanism dramatically loses its efficiency. Accordingly, we put forward a new mechanism that, despite unconstrained collusion, guarantees efficiency by providing a richer set of strategies and ensuring that it is dominant for every player to reveal truthfully not only his own valuation, but also with whom he is colluding, if he is indeed colluding with someone else. Our approach meaningfully bypasses prior impossibility proofs.