  Online auctions have expanded rapidly over the last decade and have become a
fascinating new type of business or commercial transaction in this digital era.
Here we introduce a master equation for the bidding process that takes place in
online auctions. We find that the number of distinct bidders who bid $k$ times,
called the $k$-frequent bidder, up to the $t$-th bidding progresses as
$n_k(t)\sim tk^{-2.4}$. The successfully transmitted bidding rate by the
$k$-frequent bidder is obtained as $q_k(t) \sim k^{-1.4}$, independent of $t$
for large $t$. This theoretical prediction is in agreement with empirical data.
These results imply that bidding at the last moment is a rational and effective
strategy to win in an eBay auction.
