  Blackwell approachability, regret minimization and calibration are three
criteria evaluating a strategy (or an algorithm) in different sequential
decision problems, or repeated games between a player and Nature. Although they
have at first sight nothing in common, links between have been discovered: both
consistent and calibrated strategies can be constructed by following, in some
auxiliary game, an approachability strategy. We gathered famous or recent
results and provide new ones in order to develop and generalize Blackwell's
elegant theory. The final goal is to show how it can be used as a basic
powerful tool to exhibit a new class of intuitive algorithms, based on simple
geometric properties. In order to be complete, we also prove that
approachability can be seen as a byproduct of the very existence of consistent
or calibrated strategies.

Computer Science and Game Theory