This is an important research paper devoted to the study of a class consisting in simple adaptive strategies, in the repeated play of a game, having the Hannan-consistence property. Starting from their previous Blackwell's approachability theory for games with vector payoffs, the authors offer an approachable set in vector payoff space through the agency of a special class of strategies. The general theorie is applied to the regret framework and one obtains an entire class of Hannan-consistent strategies. Explicit discussion on fictitious play is presented together with conditional regrets and correlated equilibria.