Drifting Games

We introduce and study a general, abstract game played between two players called the shepherd and the adversary. The game is played in a series of rounds using a finite set of “chips” which are moved about in ℝn. On each round, the shepherd assigns a desired direction of movement and an importance weight to each of the chips. The adversary then moves the chips in any way that need only be weakly correlated with the desired directions assigned by the shepherd. The shepherd's goal is to cause the chips to be moved to low-loss positions, where the loss of each chip at its final position is measured by a given loss function.