A seller has a fixed number of goods to sell by a deadline. At each time, he posts a regular price and decides whether to hold a flash sale. Over time, buyers privately enter the market and strategically time their purchases. If a buyer does not purchase when she arrives, she can pay an attention cost to recheck the regular price afterwards, or she can wait for future flash sales where she may obtain a good at a discounted price. In the unique Markov perfect equilibrium, the seller sporadically holds flash sales to lower the stock of goods. A flash sale increases the willingness to pay of future buyers, but decreases the willingness to pay of buyers who arrive early in the game. When it is very likely that a buyer will obtain a good in a flash sale, the seller holds a “big” initial flash sale for all but one unit of the good.

ABSTRACT We propose a theory of reputation to explain how investors rationally respond to mutual fund star ratings. A fund's performance is determined by its information advantage, which can be acquired but decays stochastically. Investors form beliefs about whether the fund is informed based on its past performance. We refer to such beliefs as fund reputation, which determines fund flows. As performance changes continuously, equilibrium fund reputation may take discrete values only and thus can be labeled with stars. Star upgrades thus imply reputation jumps, leading to discrete increases in flows and expected performance, although stars do not provide new information.