摘要：We study a dynamic market setting where an intermediary interacts with an unknown large sequence of agents that can be either sellers or buyers: their identities, as well as the sequence length n, are decided in an adversarial, online way. Each agent is interested in trading a single item, and all items in the market are identical. The intermediary has some prior, incomplete knowledge of the agents' values for the items: all seller values are independently drawn from the same distribution F_S, and all buyer values from F_B. The two distributions may differ, and we make common regularity assumptions, namely that F_B is MHR and F_S is log-concave. We focus on online, posted-price mechanisms, and analyse two objectives: that of maximizing the intermediary's profit and that of maximizing the social welfare, under a competitive analysis benchmark. First, on the negative side, for general agent sequences we prove tight competitive ratios of Theta(\sqrt(n)) and Theta(\ln n), respectively for the two objectives. On the other hand, under the extra assumption that the intermediary knows some bound \alpha on the ratio between the number of sellers and buyers, we design asymptotically optimal online mechanisms with competitive ratios of 1+o(1) and 4, respectively. Additionally, we study the model where the number of items that can be stored in stock throughout the execution is bounded, in which case the competitive ratio for the profit is improved to O(ln n).
