How to manipulate truthful prior-dependent mechanisms?

In the standard formulation of mechanism design, a key assumption is that the designer has reliable information and technology to determine a prior distribution over types of the agents. In the meanwhile, as pointed out by the Wilson’s Principle, a mechanism should reply as little as possible on the accuracy of prior type distribution. In this paper, we put forward a simple model to formalize and justify this statement. In our model, each agent has a type distribution. In addition, the agent can commit to a fake type distribution and bids consistently with respect to the fake distribution (i.e., plays some Bayes equilibrium under the fake distributions). The model is partially motivated by a recent consensus in the literature that the prior distribution should not be endogenous to the model but has to be learned by the designer from the agents’ past bids. We are interested in the equilibria of the induced distribution-committing games in several well-known mechanisms. Our results can be summarized as follows: (1) the game induced by Myerson auction under our model is strategically equivalent to the first-price auction under the standard model. Consequently, they are revenue-equivalent. (2) the second-price auction yields no less revenue than several reserve-based and virtual-value-based truthful, prior-dependent auctions, under our fake distribution model. These results complement a recent research agenda on prior-independent mechanism design. 1 ar X iv :1 60 6. 02 40 9v 2 [ cs .G T ] 1 9 Ju l 2 01 6