  Bid leakage is a corrupt scheme in a first-price sealed-bid auction in which
the procurer leaks the opponents' bids to a favoured participant. The rational
behaviour of such participant is to bid close to the deadline in order to
receive all bids, which allows him to ensure his win at the best price
possible. While such behaviour does leave detectable traces in the data, the
absence of bid leakage labels makes supervised classification impossible.
Instead, we reduce the problem of the bid leakage detection to a
positive-unlabeled classification. The key idea is to regard the losing
participants as fair and the winners as possibly corrupted. This allows us to
estimate the prior probability of bid leakage in the sample, as well as the
posterior probability of bid leakage for each specific auction.
  We extract and analyze the data on 600,000 Russian procurement auctions
between 2014 and 2018. We find that around 9% of the auctions are exposed to
bid leakage, which results in an overall 1.5% price increase. The predicted
probability of bid leakage is higher for auctions with a higher reserve price,
with too low or too high number of participants, and if the winner has met the
auctioneer in earlier auctions.
