The Internet and the Web have arguably surpassed the von Neumann Computer as the most complex computational artifacts of our times. Out of all the formidable characteristics of the Internet/Web, it seems that the most novel is its socio-economic complexity. The Internet and the Web are built, operated and used by a multitude of very diverse economic interests, which compete or collaborate in various degrees. In fact, this suggests that some very important insights about the Web may come from a fusion of ideas from Algorithms with concepts and techniques from Mathematical Economics and Game Theory. Since 2000, a new field has emerged (Algorithmic Game Theory and Computational Internet Economics), which examines exactly such ideas. We feel that this field belongs to Web Science. Some of the main topics of that field examined so far are Internet equilibria, the so called “Price of Anarchy” (a measure of loss of optimality due to selfishness [Koutsoupias,Papadimitriou (1999)], electronic markets and their equilibria, auctions, and algorithmic mechanisms design (inverse game theory or how to design a game in the net in such a clever way that individual players, motivated solely by their selfish interests, actually end up meeting the goals of the game designer!). Our paper here surveys the main concepts and results of this very promising subfield.