I will start with an introduction to evolutionary game theory, 
in particular replicator dynamics. Then recent results 
(obtained jointly with L. Imhof) on a stochastic version 
of the replicator dynamics, due to Fudenberg and Harris, 
will be discussed.

References:

Fudenberg, D. and Harris, C. (1992). Evolutionary dynamics with
aggregate shocks. J. Econom. Theory 57, 420-441.

Hofbauer, J and L. Imhof (2006): Time averages, recurrence and transience
in the stochastic replicator dynamics. Preprint

Hofbauer, J. and Sigmund, K. (1998).  Evolutionary Games and
Population Dynamics. Cambridge University Press.

Hofbauer, J. and Sigmund, K. (2003). Evolutionary game dynamics.
Bull. Amer. Math. Soc. 40, 479-519.

Imhof, L. A. (2005). The long-run behavior of the stochastic
replicator dynamics. Ann. Appl. Probab. 15, 1019-1045.