  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 standard regularity assumptions, namely
that $F_B$ is MHR and $F_S$ is log-concave.
  We study 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
$\varTheta(\sqrt{n})$ and $\varTheta(\ln n)$, 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 were
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
$O(\ln n)$.
