  Evolutionary game theory has impacted many fields of research by providing a
mathematical framework for studying the evolution and maintenance of social and
moral behaviors. This success is owed in large part to the demonstration that
the central equation of this theory - the replicator equation - is the
deterministic limit of a stochastic imitation (social learning) dynamics. Here
we offer an alternative elementary proof of this result, which holds for the
scenario where players compare their instantaneous (not average) payoffs to
decide whether to maintain or change their strategies, and only more successful
individuals can be imitated.
