The Price of Prior Dependence in Auctions

In the standard form 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 rely as little as possible on the prior type distribution. In this paper, we put forward a simple model to formalize this statement. In our model, each agent has a true type distribution, according to which his type is drawn. In addition, the agent is able to commit to a fake type distribution and bids rationally as if his type were from the fake distribution (e.g., plays a Bayes equilibrium under the fake distributions). We investigate the equilibria of the induced distribution-reporting games among bidders, under the context of single-item auctions. We obtain several interesting findings: (1) the game induced by Myerson auction under our model is strategically equivalent to the first-price auction under the standard model. Consequently, the two games are revenue-equivalent. (2) the second-price auction, a well known prior independent auction, yields (weakly) more revenue than several reserve-based and virtual-value-based truthful, prior-dependent auctions, under our model. Our results complement the current literature which aims to show the superiority of prior-independent mechanisms.