Collusive dominant-strategy truthfulness

We show that collusion and wrong beliefs may cause a dramatic efficiency loss in the Vickrey mechanism for auctioning a single good in limited supply. We thus put forward a new mechanism guaranteeing efficiency in a very adversarial collusion model, where the players can partition themselves into arbitrarily many coalitions, exchange money with each other, and perfectly coordinate their actions. Our mechanism bypasses classic impossibility results (such as those of Green and Laffont, and of Schummer) by providing the players with a richer set of strategies, making it dominant for every coalition C to instruct each of its members to report truthfully not only his own valuation, but also his belonging to C. Our mechanism is coalitionally rational, which implies being individually rational for independent players.