Continuous and Global Stability in Innovative Evolutionary Dynamics

Innovation plays a central role in the development of modern economies, as does the regret of those who have missed the opportunity to try a successful new strategy. In contrast to purely biological environments, where new strategies emerge mainly by random mutation, human societies tend to exhibit more deliberate, although possibly imperfect inventions of new strategies. In this paper, we study such a class of evolutionary dynamics for the case of continuous strategy spaces, the Brown–von Neumann–Nash dynamics. For two general classes of games, we establish global convergence to Nash equilibria that are continuously stable or evolutionarily robust. Journal of Economic Literature Classification Numbers: C70, 72.