The theoretical literature on innovation has been concerned with a single innovation produced by a number of identical agents. By contrast, we consider a market in which one firm is the current incumbent, while the remaining firms are challengers. Moreover, we consider a sequence of innovations, so that success does not imply that the successful firm reaps monopoly profits forever after, but only until the next, better innovation is developed. We begin with a fully optimizing behavioral model and derive the equivalent of the Schumpeterian “process of creative destruction.” That is, a firm enjoys temporary monopoly power but is soon overthrown by a more inventive challenger.