  We report statistical regularities of the opening and closing auctions of
French equities, focusing on the diffusive properties of the indicative auction
price. Two mechanisms are at play as the auction end time nears: the typical
price change magnitude decreases, favoring underdiffusion, while the rate of
these events increases, potentially leading to overdiffusion. A third
mechanism, caused by the strategic behavior of traders, is needed to produce
nearly diffusive prices: waiting to submit buy orders until sell orders have
decreased the indicative price and vice-versa.
