  In evolutionary games the fitness of individuals is not constant but depends
on the relative abundance of the various strategies in the population. Here we
study general games among n strategies in populations of large but finite size.
We explore stochastic evolutionary dynamics under weak selection, but for any
mutation rate. We analyze the frequency dependent Moran process in well-mixed
populations, but almost identical results are found for the Wright-Fisher and
Pairwise Comparison processes. Surprisingly simple conditions specify whether a
strategy is more abundant on average than 1/n, or than another strategy, in the
mutation-selection equilibrium. We find one condition that holds for low
mutation rate and another condition that holds for high mutation rate. A linear
combination of these two conditions holds for any mutation rate. Our results
allow a complete characterization of n*n games in the limit of weak selection.

Populations and Evolution