Landscapes: A Natural Extension of Search Theory

Abstract

Technological change at the firm-level has commonly been modeled as random sampling from a fixed distribution of possibilities. Such models typically ignore empirically important aspects of the firm's search process, namely the related observations that a firm's current technology constrains future innovation and that firms' technological search tends to be local in nature. In this paper we explicitly treat these aspects of the firm's search for technological improvements by introducing a technology landscape into the search-theoretic framework. Technological search is modeled as movement over a technology landscape with the firm's adaptive walk constrained by the firm's location on the landscape, the correlation structure of the landscape and the cost of innovation. We show that the standard search model is attained as a limiting case of a more general landscape search model. We obtain two key results, otherwise unavailable in the standard search model: the presence of local optima in space of technological possibilities and the determination of the optimal search distance. We find that early in the search for technological improvements, if the initial position is poor or average, it is optimal to search far away on the technology landscape; but as the firm succeeds in finding technological improvements it is optimal to confine search to a local region of the landscape. Notably, we obtain diminishing returns to search without having to make the assumption that the firm's repeated draws from the search space are independent and identically distributed. The distinction between dramatic technological improvements ("innovations") and minor technological improvements hinges on the distance at which a firm decides to sample the technology landscape.