  Recently, there is growing interest and need for dynamic pricing algorithms,
especially, in the field of online marketplaces by offering smart pricing
options for big online stores. We present an approach to adjust prices based on
the observed online market data. The key idea is to characterize optimal prices
as minimizers of a total expected revenue function, which turns out to be
convex. We assume that consumers face information processing costs, hence,
follow a discrete choice demand model, and suppliers are equipped with quantity
adjustment costs. We prove the strong smoothness of the total expected revenue
function by deriving the strong convexity modulus of its dual. Our
gradient-based pricing schemes outbalance supply and demand at the convergence
rates of $\mathcal{O}(\frac{1}{t})$ and $\mathcal{O}(\frac{1}{t^2})$,
respectively. This suggests that the imperfect behavior of consumers and
suppliers helps to stabilize the market.
