Online algorithms for the general k-search problem

This paper investigates the general k-search problem, in which a player is to sell totally k units of some asset within n periods, aiming at maximizing the total revenue. At each period, the player observes a quoted price which expires before the next period, and decides irrecoverably the amount of the asset to be sold at the price. We present a deterministic online algorithm and prove it optimal for the case where k≤n-1. For the other case where k≥n, we show by numerical illustration that the gap between the upper and the lower bound of competitive ratio is quite small for many situations.