Optimal search on a technology landscape

We address the question of how a firm's current location in the space of technological possibilities constrain its search for technological improvements. We formalize a quantitative notion of distance between technologies - encompassing the distinction between evolutionary changes (small distance) versus revolutionary change (large distance) - and introduce a technology landscape into an otherwise standard dynamic programming setting where the optimal strategy is to assign a reservation price to each possible technology. Technological search is modeled as movement, constrained by the cost of search, on a technology landscape. Simulations are presented on a stylized technology landscape while analytic results are derived using landscapes that are similar to Markov random fields. 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.