Regret in the on-line decision problem

At each point in time a decision maker must make a decision. The payoff in a period from the decision made depends on the decision as well as on the s tale of the world that obtains at that time. The difficulty is that the dec ision must be made in advance of any knowledge, even probabilistic, about w hich state of the world will obtain. A range of problems from a variety of disciplines can be framed in this way. In this paper we survey the main res ults obtained, as well as some of their applications. Journal of Economic L iterature Classification Numbers: C70, C73. (C) 1999 Academic Press.