From my brief reading, this paper essentially deals with solving an information asymmetry. The males don't know if the females are willing to mate, and the females don't know if the males intend to stay around. Thus, gifts are used as signals that indicate, through a game-theoretic mechanism, the unknown values.

It's strange, then, that the paper doesn't look to the field of information asymmetry in economics, which is a fairly well-developed field at this point and more or less addresses all of the issues considered in this paper. Signaling is well-known as an approach to solving information asymmetries (a second approach is warranties).