  In evolutionary game dynamics, reproductive success increases with the
performance in an evolutionary game. If strategy $A$ performs better than
strategy $B$, strategy $A$ will spread in the population. Under stochastic
dynamics, a single mutant will sooner or later take over the entire population
or go extinct. We analyze the mean exit times (or average fixation times)
associated with this process. We show analytically that these times depend on
the payoff matrix of the game in an amazingly simple way under weak selection,
ie strong stochasticity: The payoff difference $\Delta \pi$ is a linear
function of the number of $A$ individuals $i$, $\Delta \pi = u i + v$. The
unconditional mean exit time depends only on the constant term $v$. Given that
a single $A$ mutant takes over the population, the corresponding conditional
mean exit time depends only on the density dependent term $u$. We demonstrate
this finding for two commonly applied microscopic evolutionary processes.
