Sequential common-value auctions with asymmetrically informed bidders

We study an infinitely repeated first-price auction with common values. We focus on one-sided incomplete information, in which one bidder learns the objects' value, which itself does not change over time. Learning by the uninformed bidder occurs only through observation of the bids. The proprietary information is eventually revealed, and the seller extracts essentially the entire rent (for large discount factors). Both players' pay-offs tend to 0 as the discount factor tends to 1. However, the uninformed bidder does relatively better than the informed bidder. We discuss the case of two-sided incomplete information and argue that, under a Markovian refinement, the outcome is pooling as information is revealed only insofar as it does not affect prices.