We live in strange times. A machine plays the strategy game Go better than any human; upstarts like Apple and Google destroy industry stalwarts such as Nokia; ideas from the crowd are repeatedly more innovative than corporate research labs.

MIT's Andrew McAfee and Erik Brynjolfsson know what it takes to master this digital-powered shift: we must rethink the integration of minds and machines, of products and platforms, and of the core and the crowd. In all three cases, the balance now favors the second element of the pair, with massive implications for how we run our companies and...