We consider a two person perfect information game with a buffer. On each round, Player I selects a vectorvRnwith v1, where is thel2-norm, and Player II can either put the vector in the buffer or choose a sign i=1 for a given vectorvi. There are no more thandvectors that can be put in the buffer. Player II's object is to keep the cumulative sum ivi as small as possible. We prove that the value of the game goes to infinity ifdn-2. We give an upper bound of the value ifdn-1. The same results hold for a generalized problem. 1998 Academic Press.
