What is the overlap between the Gaia and the Hipparcos catalog?
As part of the Gaia DR2, cross-matches to several catalogues including HIP2 were included. The main reference for this is Marrese et al. (2018) "Gaia Data Release 2. Cross-match with external catalogues: algorithms and results". The resultant matches are included in the tables gaiadr2.hipparcos2_best_neighbour and gaiadr2.hipparcos2_neighbourhood available via the query facilities in the Gaia Archive.

Unfortunately the match is not particularly complete and it is not entirely clear why. From the paper:


  While we expect to find Gaia counterparts for most of the Hipparcos2 sources, with the exception of the brightest ones, the
  cross-match results include only about two-thirds of them. This
  means that according to the adopted cross-match algorithm, only
  about two-thirds of the Hipparcos2 objects have a Gaia counterpart that is compatible within the position errors (i.e. have at least
  one good neighbour). Hence the Hipparcos2 cross-match results
  clearly show an issue that needs to be investigated.


As a result, they also provide a table of cross-matches based on a 1-arcsecond cone search, available on the Gaia DR2 known issues page. This cross-match is a lot more complete, but there are still a few objects that are present in both catalogues that are missing. Several of these are nevertheless present in SIMBAD, e.g. 85&nbsp;Pegasi = HIP&nbsp;171 = Gaia&nbsp;DR2&nbsp;2853900872207150720.