Chaos and unpredictability in game theory

A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ
from those of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior
replace the usual fixed-point population solutions. We observe the familiar period-doubling and chaotic-bandsplitting
attractor cascades of unimodal maps but in some cases more elaborate variations appear due to
bimodality. Also unphysical stationary solutions can have unusual physical implications, such as the uncertainty of
final population caused by sensitivity to initial conditions and fractality of attractor preimage manifolds.
A general introduction to game theory and evolutionary dynamics will be given at the beginning of the talk.