Recombinant Search

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Joint with Steven Callander

Abstract: As noted by Weitzman (1998), the search for new ideas, technologies, and products is often combinatorial: familiar ideas are combined in novel ways to expand knowledge. We present a model of directed Bayesian search over a multi-dimensional idea landscape, with ideas spanning both individual fields of knowledge and combinations of distinct fields. Success is modeled through the sample paths of the Brownian staple, a natural extension of Callander’s (2011) Brownian motion framework to higher dimensions. We characterize prediction and optimal search by a sequence of short-lived researchers. Prediction is complex: predicting a target idea from a given history generically involves the entire set of ideas previously explored. The analysis highlights the critical role of derivative research in reducing such predictive complexity and enabling search at the frontiers. Moreover, recombinant search is gradual and proceeds in a grid of existing knowledge:  it pushes the frontier of at most one field at a time, combining a familiar idea from one field with an unfamiliar one in the other. These dynamics are consistent with observed patterns in patent innovation.