We address the problem of learning and implementation on the Internet. When agents play repeated games in distributed environments like the Internet, they have very limited {\em a priori} information about the other players and the payoff matrix, and the play can be highly asynchronous. Consequently, standard solution concepts like Nash equilibria, or even the serially undominated set, do not apply in such a setting. To construct more appropriate solution concepts, we first describe the essential properties that constitute ``reasonable'' learning behavior in distributed environments. We then study the convergence behavior of such algorithms; these results lead us to propose rather non traditional solutions concepts for this context. Finally, we discuss implementation of social choice functions with these solution concepts.
