[R] how to combine two data frames via factors (or somehow else)

[Philipp Chapkovski]

Hello!
The question should be very naive, but I am a beginner and stuck with
this unfortunately.
There is a dataset of people's affiliation to companies that looks
like that (a data frame actually)
  x y
1 a X
2 b X
3 c X
4 f Z
5 e Z
6 g Z
where x is a name of a person and y is a company name. That is, a,b,c
work in a company X. f,e,g work in a company Z.

and there is another dataset with the affiliation of companies. Like
that (much much longer in reality):
  y1 y2
1  X W
2  Z W
that means that both X and Z belongs to the same company W.
What is the most compact way (without loops etc) to 'attach' the 'head
company' from the second dataset to the first dataset so I can have
something like:

  x  y owner
1 a X W
...
4 f  Z W

I know it should be done somehow with factors, but I don't know how.
Thank you in advance!