Epsilon-stability and the speed of learning in network games

This paper introduces epsilon-stability as a generalization of the
concept of stochastic stability in learning and evolutionary game
dynamics. An outcome of a model of stochastic evolutionary dynamics is
said to be epsilon-stable in the long-run if for a given model of
mistakes it maximizes its invariant distribution. We construct an
efficient algorithm for computing epsilon-stable outcomes and provide
conditions under which epsilon-stability can be approximated by
stochastic stability. We also define and provide tighter bounds for
contagion rate and metastability as measures for characterizing the
short-run and medium-run behaviour of a typical stochastic evolutionary
model.

Keywords: Stochastic evolution, network games, epsilon-stable sets, expected
waiting time, metastability, contagion rate.