Worst performance of Hedge in short games

Hedge has been proposed as an adaptive scheme, which guides an agent's decision in resource selection and distribution problems in the areas of computer and communication networks, e.g. network path selection, load distribution, network interdiction, and also in problems in the area of transportation. Hedge dictates a decision based on the performance of a number of past similar decisions. Under certain conditions Hedge is known to provide an asymptotically optimal series of decisions. We perform an exact worst case analysis of the Hedge algorithm when it is used in instances with a small number of rounds.