The payoff matrix of a finite stage game is realized randomly, and then the stage game is repeated infinitely. The distribution over states of the world (a state corresponds to a payoff matrix) is commonly known, but players do not observe nature’s choice. Over time, they can learn the state...

We characterize an optimal mechanism for a seller with one unit of a good facing N ≥ 3 buyers and a single competitor who sells another identical unit in a second-price auction. Buyers who do not get the seller's good compete in the competitor's subsequent auction. The mechanism features...