In this paper, we consider a multi-unit Dutch auction over the Internet where auctioneer gradually decrements per unit price of the item during the course of the auction. We investigate an optimal price control problem of the auctioneer, that is, the problem of finding a decrementing price sequence that maximizes his total expected revenue in the presence of uncertainty with regard to arrival pattern of bidders and their individual price-demand curves. We start with an analysis of an analogous multi-unit pay-your-bid auction in a discrete setting and provide a characterization of mixed strategy equilibrium. Since it is difficult to arrive at a pure strategy equilibrium, we deviate from game theoretic consideration and model the above decision problem in a Dutch auction as a single-agent Reinforcement Learning in an uncertain non-stationary auction environment wherein the auctioneer (or his agent) uses its experience interacting with the environment to improve his (its) pricing strategies.