Beyond replicator dynamics: Innovation-selection dynamics and optimal diversity

We propose a new evolutionary approach to model technological change based on an extension of replicator dynamics with recombination and mutation. It gives rise to interactive innovation-selection dynamics. The model allows studying the combined effects of selection and variety generation on evolutionary-economic change. The developed framework describes a population of boundedly rational entrepreneurs who decide each period on the allocation of investments in different production technologies. They tend to invest in below-average cost technologies, just as under replicator dynamics. In addition, they spend a constant fraction of investments, captured by mutation and recombination rates, on alternative technologies and research on recombinant innovation. As opposed to most previous studies, mutation and recombination are here conceptual variables with a concrete behavioral interpretation, namely describing the decision rules (heuristics) of investors. We compare the dynamics of shares of investments in various technologies for three cases: with constant costs of capital, with costs decreasing steadily and exogenously over time, and with costs depending on the level of cumulative investments. For each model version, we examine under which conditions the coexistence of technological options is feasible and optimal in terms of minimizing the average cost of investments.