Stability and strategic diffusion in networks

Learning and stochastic evolutionary models provide a useful framework for analyzing repeated interactions and experimentation among economic agents over time. They also provide sharp predictions about equilibrium selection when multiplicity exists. This paper defines three convergence measures, diffusion rate, expected waiting time and convergence rate, for characterizing the short-run, medium-run and long-run behavior of a typical model of stochastic evolution. We provide tighter bounds for each without making restrictive assumptions on the model and amount of noise as well as interaction structure. We demonstrate how they can be employed to characterize evolutionary dynamics for coordination games and strategic diffusion in networks. Application of our results to strategic diffusion gives insights on the role played by the network topology. For example we show how networks made up of cohesive subgroups speed up evolution between quasi-stable states while sparsely connected networks have the opposite effect of favoring almost global stability.

Keywords: Learning and evolution, networks, diffusion rate, convergence rate, expected waiting time

JEL Classification: C73, D80 034