BALANCING GAME WITH A BUFFER

We consider a two person perfect information game with a buffer. On ea ch round, Player I selects a vector v is an element of R-n with \v\ le ss than or equal to 1, where \.\ is the l(2)-norm, and Player II can e ither put the vector in the buffer or choose a sign epsilon(i) = +/-1 for a given vector v(i). There are no more than d vectors that can be put in the buffer. Player II's object is to keep the cumulative sum \S igma epsilon(i)v(i)\ as small as possible. We prove that the value of the game goes to infinity if d less than or equal to n - 2.We give an upper bound of the value if d greater than or equal to n - 1. The same results hold for a generalized problem. (C) 1998 Academic Press.