2003): “Private information in repeated auctions

We study an infinitely repeated two-player game with incomplete information, where the stage game is a first-price auction with pure common values. Before playing, the bidders receive affiliated private signals about the value, which itself does not change over time. Items sold in such an auction environment include bonds, wine, neighboring oil tracts, and wholesale fish. In this setting, learning occurs only through observation of the bids. We show that in the case of one-sided incomplete information, this information is eventually revealed and the seller extracts essentially the entire rent (for large enough discount factors). In contrast, the unique equilibrium with patient players under two-sided incomplete information is purely pooling: no information is ever revealed. In the special case with only two types of each bidder, we are able to fully characterize the equilibrium for all values of the discount factor and all priors.