  Dynamical mechanisms that can stabilize the coexistence or diversity in
biology are generally of fundamental interest. In contrast to many two-strategy
evolutionary games, games with three strategies and cyclic dominance like the
rock-paper-scissors game (RPS) stabilize coexistence and thus preserve
biodiversity in this system. In the limit of infinite populations, resembling
the traditional picture of evolutionary game theory, replicator equations
predict the existence of a fixed point in the interior of the phase space. But
in finite populations, strategy frequencies will run out of the fixed point
because of stochastic fluctuations, and strategies can even go extinct. For
three different processes and for zero-sum and non-zero-sum RPS as well, we
present results of extensive simulations for the mean extinction time (MET),
depending on the number of agents N, and we introduce two analytical approaches
for the derivation of the MET.
