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